Trắc nghiệm Nguyên hàm Toán Lớp 12

A. 244

B. 247

C. 245

D. 246

A. $\frac{{{x^2} + x - 1}}{{x + 1}}$

B. $\frac{{{x^2} - x - 1}}{{x + 1}}$

C. $\frac{{{x^2} + x+ 1}}{{x + 1}}$

D. $\frac{{{x^2} }}{{x + 1}}$

A. $\frac{2}{3}\ln \left| {2x + 1} \right| + \frac{5}{3}\ln \left| {x - 1} \right| + C$

B. $-\frac{2}{3}\ln \left| {2x + 1} \right| + \frac{5}{3}\ln \left| {x - 1} \right| + C$

C. $\frac{2}{3}\ln \left| {2x + 1} \right| - \frac{5}{3}\ln \left| {x - 1} \right| + C$

D. $\frac{1}{3}\ln \left| {2x + 1} \right| + \frac{5}{3}\ln \left| {x - 1} \right| + C$

A. $F\left( x \right) = \frac{{3{x^2}}}{4} + \frac{3}{{2x}} + \frac{7}{4}$

B. $F\left( x \right) = \frac{{3{x^2}}}{4} - \frac{3}{{2x}} - \frac{7}{4}$

C. $F\left( x \right) = \frac{{3{x^2}}}{4} + \frac{3}{{2x}} - \frac{7}{4}$

D. $F\left( x \right) = \frac{{3{x^2}}}{4} + \frac{3}{{2x}} + \frac{1}{4}$

A. $F(x) = 3{x^2} - \frac{{\cos 3x}}{3} + \frac{2}{3}.$

B. $F(x) = 3{x^2} - \frac{{\cos 3x}}{3} -1$

C. $F(x) = 3{x^2} + \frac{{\cos 3x}}{3} + 1$

D. $F(x) = 3{x^2} - \frac{{\cos 3x}}{3} +1$

A. 3

B. 4

C. 6

D. 8

A. $F\left( x \right) = \frac{8}{5}{\left( {2x - 1} \right)^{\frac{5}{4}}} + C.$

B. $F\left( x \right) = \frac{2}{5}{\left( {2x - 1} \right)^{\frac{5}{4}}} + C.$

C. $F\left( x \right) = {\left( {2x - 1} \right)^{\frac{5}{4}}} + C.$

D. $F\left( x \right) = \frac{1}{5}{\left( {2x - 1} \right)^{\frac{5}{4}}} + C.$

A. $2x\sqrt x + \frac{{3{x^2}}}{2} + C$

B. $\frac{4}{3}x\sqrt x + \frac{{3{x^2}}}{2} + C$

C. $\frac{3}{2}x\sqrt x + \frac{{3{x^2}}}{2} + C$

D. $4x\sqrt x + \frac{{3{x^2}}}{2} + C$

A. $\smallint f(x)dx = \frac{{{x^3}}}{3} - \frac{2}{x} + C.$

B. $\smallint f(x)dx = \frac{{{x^3}}}{3} +\frac{2}{x} + C.$

C. $\smallint f(x)dx = \frac{{{x^3}}}{3}+ \frac{1}{x} + C.$

D. $\smallint f(x)dx = \frac{{{x^3}}}{3}+ \frac{2}{x} + C.$

A. $- 3\sin x + \frac{1}{x} + C$

B. $- 3\sin x - \frac{1}{x} + C$

C. $3\cos x + \frac{1}{x} + C$

D. $3cos x +ln x + C$

A. Cả hai đều sai

B. Cả hai đều đúng

C. An đúng, Bình sai

D. Bình đúng, An sai

A. $\smallint f\left( x \right){\rm{d}}x = - 2\ln \left| {1 - 2x} \right| + C.$

B. $\smallint f\left( x \right){\rm{d}}x = 2\ln \left| {1 - 2x} \right| + C.$

C. $\smallint f\left( x \right){\rm{d}}x = - \frac{1}{2}\ln \left| {1 - 2x} \right| + C.$

D. $\smallint f\left( x \right){\rm{d}}x = \ln \left| {1 - 2x} \right| + C.$

A. $\frac{2}{3}{x^6} - \ln x + 2018x + C$

B. $20{x^4} + \frac{1}{{{x^2}}} + C$

C. $\frac{2}{3}{x^6} - \ln \left| x \right| + 2018x + C$

D. $\frac{4}{6}{x^6} + \ln \left| x \right| + 2018x + C$

A. $\smallint \frac{2}{{4x - 3}}{\mkern 1mu} {\rm{d}}x = 2\ln \left( {2x - \frac{3}{2}} \right) + C.$

B. $\smallint \frac{2}{{4x - 3}}{\mkern 1mu} {\rm{d}}x = \frac{1}{4}\ln \left| {4x - 3} \right| + C.$

C. $\smallint \frac{2}{{4x - 3}}{\mkern 1mu} {\rm{d}}x = \frac{1}{2}\ln \left| {2x - \frac{3}{2}} \right| + C.$

D. $\smallint \frac{2}{{4x - 3}}{\mkern 1mu} {\rm{d}}x = \frac{1}{2}\ln \left( {2x - \frac{3}{2}} \right) + C.$

A. $\smallint \frac{1}{{x + 2}}dx = \ln \left( {x + 2} \right) + C$

B. y=ln⁡(3|x+2|) là một nguyên hàm của f(x)

C. y=ln⁡|x+2|+C là họ nguyên hàm của f(x)

D. y=ln⁡|x+2| là một nguyên hàm của f(x)

A. $\frac{{{x^4}}}{4} + \frac{{{x^3}}}{2} + C$

B. $\frac{{{x^4}}}{4} + \frac{{{x^3}}}{2} +x+ C$

C. $x^4 + \frac{{{x^3}}}{2} +x+ C$

D. $3x^3+C$

A. ${x^2}\left( {1 + \frac{3}{4}{x^2}} \right) + C$

B. $\frac{{{x^2}}}{2}\left( {2x + {x^3}} \right) + C$

C. ${x^2}\left( {2 + 6x} \right) + C$

D. ${x^2} + \frac{3}{4}{x^4}$

A. $F\left( x \right) = {e^x} - 2019$

B. $F\left( x \right) = x^2+{e^x} - 2019$

C. $F\left( x \right) = x^2+{e^x} +2017$

D. $F\left( x \right) = x^2+{e^x} +2018$

A. ln⁡2                                   

B. 2ln⁡4                                 

C. ln⁡3                                  

D. 2ln2

A. $F\left( x \right) = - \frac{1}{{2018}}{e^{ - 2018x + 2017}} + \frac{1}{{2018e}}$

B. $F\left( x \right) = - \frac{1}{{2018}}{e^{ - 2018x + 2017}} +e+ \frac{1}{{2018e}}$

C. $F\left( x \right) = -2018{e^{ - 2018x + 2017}} +e+ \frac{1}{{2018e}}$

D. $F\left( x \right) = -2018{e^{ - 2018x + 2017}} + \frac{1}{{2018e}}$

A. F(x)=tan⁡x−1                                       

B. F(x)=−tan⁡x                 

C. F(x)=tan⁡x+1           

D. F(x)=−tanx+1

A. $F\left( x \right) = \frac{1}{{\sqrt 3 }} - \cot x$

B. $F\left( x \right) =\sqrt 3 - \cot x$

C. $F\left( x \right) = \frac{{\sqrt 3 }}{2} - \cot x$

D. $F\left( x \right) = - \cot x+C$

A. $\smallint f\left( x \right)dx = \frac{1}{5}\sin 5x + C$

B. $\smallint f\left( x \right)dx = \sin 5x + C$

C. $\smallint f\left( x \right)dx = -5\sin 5x + C$

D. $\smallint f\left( x \right)dx = -\frac{1}{5}\sin 5x + C$

A. $\mathop \smallint \limits_{}^{} f\left( x \right)dx = \frac{{{x^2}}}{2} + \sin x + C$

B. $\mathop \smallint \limits_{}^{} f\left( x \right)dx = 1 - \sin x + C$

C. $\mathop \smallint \limits_{}^{} f\left( x \right)dx = x\sin x + \cos x + C$

D. $\mathop \smallint \limits_{}^{} f\left( x \right)dx = \frac{{{x^2}}}{2} - \sin x + C$

A. $\frac{x}{2} + \frac{{\sin 2x}}{4} + C.$

B. $\frac{x}{2} + \frac{{\sin 2x}}{2} + C.$

C. $\frac{x}{2} - \frac{{\sin 2x}}{4} + C.$

D. $\frac{x}{2} - \frac{{\sin 2x}}{2} + C.$

A. $\smallint \frac{1}{{{{\cos }^2}x}}dx = \tan x + C$

B. $\smallint \frac{1}{{{{\sin }^2}x}}dx = \cot x + C$

C. $\smallint \frac{1}{{{{\sin }^2}x}}dx = - \cot x + C$

D. $\smallint \frac{1}{{{{\cos }^2}x}}dx = \frac{{\sin x}}{{\cos x}} + C$

A. $\smallint f\left( x \right)dx = \frac{{{x^4}}}{4} - \frac{3}{x} + \frac{{{2^x}}}{{\ln 2}} + C$

B. $\smallint f\left( x \right)dx = \frac{{{x^4}}}{4}+ \frac{3}{x} + \frac{{{2^x}}}{{\ln 2}} + C$

C. $\smallint f\left( x \right)dx = \frac{{{x^4}}}{4} - \frac{3}{x} +2^x+ C$

D. $\smallint f\left( x \right)dx = \frac{{{x^4}}}{4}+ \frac{3}{x} +2^x+ C$

A. $\smallint f(x)dx = {e^{2018x}} + C.$

B. $\smallint f(x)dx = \frac{1}{{2018}}{e^{2018x}} + C.$

C. $\smallint f(x)dx = 2018{e^{2018x}} + C.$

D. $\smallint f(x)dx = {e^{2018x}}.\ln 2018 + C.$

A. $I = \frac{{\ln 2}}{2} + \frac{{\ln 3}}{3} + C.$

B. $I = \frac{{\ln 2}}{2^x} + \frac{{\ln 3}}{3^x} + C.$

C. $I = \frac{{{2^x}}}{{\ln 2}} + \frac{{{3^x}}}{{\ln 3}} + C.$

D. $I = - {\mkern 1mu} \frac{{\ln 2}}{2} - \frac{{\ln 3}}{3} + C.$

A. $\frac{{{{2018}^x}}}{{\log 2018}} + C.$

B. $\frac{{{{2018}^{x\, + \,1}}}}{{x + 1}} + C.$

C. $\frac{{{{2018}^x}}}{{\ln 2018}} + C.$

D. $2018^x.ln2018+C.$

A. $F(x) = 1 + \frac{{{2^x}}}{{\ln 2}} + C$

B. $F(x) = \frac{{{x^2}}}{2} + {2^x}\ln 2 + C$

C. $F(x) = \frac{{{x^2}}}{2} + {2^x} + C$

D. $F(x) = \frac{{{x^2}}}{2} + \frac{{{2^x}}}{{\ln 2}} + C$

A. $y = - 4{e^{1 - 4x}}$

B. $y = \frac{1}{4}{e^{1 - 4x}}$

C. $y = - \frac{1}{4}{e^{1 - 4x}}$

D. ${e^{1 - 4x}}$

A. $\smallint f\left( x \right)dx = {3^x} + C$

B. $\smallint f\left( x \right)dx = {3^x}ln3 + C$

C. $\smallint f\left( x \right)dx = \frac{{{3^{x + 1}}}}{{x + 1}} + C$

D. $\smallint f\left( x \right)dx = \frac{{{3^x}}}{{\ln 3}} + C$

A. $\smallint {a^x}dx = \frac{{{a^x}}}{{\ln a}} + C(0 < a \ne 1)$

B. $\smallint {a^x}dx = a^x + C(0 < a \ne 1)$

C. $\smallint {a^x}dx =a^x\ln a + C(0 < a \ne 1)$

D. $\smallint {a^x}dx =a^xln a (0 < a \ne 1)$

A. $\smallint {e^x}{\mkern 1mu} {\rm{d}}x = {e^x} + C.$

B. $\smallint 0{\mkern 1mu} {\rm{d}}x = C.$

C. $\smallint \frac{1}{x}{\mkern 1mu} {\rm{d}}x = \ln x + C.$

D. $\smallint {\rm{dx}} = x + C.$

A. ∫0dx=C       

B. ∫dx=C         

C. ∫dx=0          

D. ∫0dx=x+C

A. F(x)=5−cos⁡x là một nguyên hàm của hàm số f(x)=sinx

B. Nếu F(x) là một nguyên hàm của hàm số f(x) thì mọi nguyên hàm của f(x) đều có dạng F(x)+C (C là hằng số).

C. $\mathop \smallint \limits_{}^{} \frac{{u'\left( x \right)}}{{u\left( x \right)}}dx = \log \left| {u\left( x \right)} \right| + C$

D. F(x)=x2 là một nguyên hàm của f(x)=2x

A. $\smallint \frac{1}{x}{\mkern 1mu} {\rm{d}}x = \ln \left| x \right|.$

B. $\smallint \frac{1}{x}{\mkern 1mu} {\rm{d}}x = \ln \left| x \right|.+C$

C. $\smallint \frac{1}{x}{\mkern 1mu} {\rm{d}}x = - \frac{1}{{{x^2}}} + C.$

D. $\smallint \frac{1}{x}{\mkern 1mu} {\rm{d}}x = \ln x+C$

A. $\smallint \sin xdx = \cos x + C$

B. $\smallint dx = x + C$

C. $\smallint {e^x}dx = {e^x} + C$

D. $\smallint \frac{1}{x}dx = \ln \left| x \right| + C$

A. y=tan⁡x                             

B. y=cot⁡x

C. y=sin⁡x                              

D. y=−sinx

A. $\smallint \sin 2x{\mkern 1mu} {\rm{d}}x = - \frac{{\cos 2x}}{2} + C.$

B. $\smallint \sin 2x{\mkern 1mu} {\rm{d}}x = - \cos 2x + C.$

C. $\smallint \sin 2x{\mkern 1mu} {\rm{d}}x = \frac{{\cos 2x}}{2} + C.$

D. $\smallint \sin 2x{\mkern 1mu} {\rm{d}}x =2 \cos 2x + C.$

A. $- \sin 2x + C$

B. $-2 \sin 2x + C$

C. $\sin 2x + C$

D. $2 \sin 2x + C$

A. $\smallint \cos 2x{\rm{d}}x = 2\sin 2x + C.$

B. $\smallint \cos 2x{\rm{d}}x = - \frac{1}{2}\sin 2x + C.$

C. $\smallint \cos 2x{\rm{d}}x = \sin 2x + C.$

D. $\smallint \cos 2x{\rm{d}}x = \frac{1}{2}\sin 2x + C.$

A. $5cos 5 x + C .$

B. $- \frac{1}{5}\cos 5x + 2x + C.$

C. $\frac{1}{5}\cos 5x + 2x + C.$

D. $cos 5 x + 2 x + C$

A. $− 3 sin 3 x + C$

B. $- \frac{1}{3}\sin 3x + C$

C. $− sin 3 x + C$

D. $\frac{1}{3}\sin 3x + C$

A. $f\left( x \right) = \frac{{\sin 3x}}{3}$

B. $f\left( x \right) = -3sin3x$

C. $f\left( x \right) = 3sin3x$

D. $f\left( x \right) = -sin3x$

A. ${x^2} - \frac{1}{2}\cos 2x + C$

B. ${x^2} + \frac{1}{2}\cos 2x + C$

C. ${x^2} - 2xcos 2x + C$

D. ${x^2} +2cos 2x + C$

A. y=sin⁡x+1         

B. y=cos⁡x   

C. y=cot⁡x

D. y=−cosx

A. $- {x^4} + C$

B. $- \frac{{{x^4}}}{4} + x + C$

C. $- 12{x^2} + C$

D. $- {x^4} + x + C$

A. $f\left( x \right) = 12{x^2} - 6x + 2 + C$

B. $f\left( x \right) = 12{x^2} - 6x + 2$

C. $f\left( x \right) = {x^4} - {x^3} + {x^2} + Cx$

D. $f\left( x \right) = {x^4} - {x^3} + {x^2} + Cx+C'$