Tính tích phân \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqaMPevLHfij5gC1rhimfMBNvxyNvga7LupCLMB0X % fBP1wA0n3x7btFEThxMjxyJThxWLgi9Thn913E7Thx0fMBG0Nx7jtF % 91hEKHxFamXvP5wqSXMqHnxAJn0BKvguHDwzZbqefqvATv2CG4uz3b % IuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfga % saacH8YjY-vipgYlh9vqqj-hEeeu0xXdbba9frFj0-OqFfea0dXdd9 % vqai-hGuQ8kuc9pgc9q8qqaq-dir-f0-yqaiVgFr0xfr-xfr-xb9ad % baqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8qacaWGjb % Gaeyypa0Zaa8qCa8aabaWdbiGacshacaGGHbGaaiOBa8aadaahaaWc % beqaa8qacaaIYaaaaaWdaeaapeGaaGimaaWdaeaapeWaaSaaa8aaba % Wdbiabec8aWbWdaeaapeGaaGinaaaaa0Gaey4kIipakiaadIhacaqG % KbGaamiEaaaa!61F8! I = \int\limits_0^{\frac{\pi }{4}} {{{\tan }^2}} x{\rm{d}}x\)

Ta có \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqaMPevLHfij5gC1rhimfMBNvxyNvga7LupCLMB0X % fBP1wA0n3x7btFEThxMjxyJThxWLgi9Thn913E7Thx0fMBG0Nx7jtF % 91hEKHxFamXvP5wqSXMqHnxAJn0BKvguHDwzZbqefqvATv2CG4uz3b % IuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfga % saacH8YjY-vipgYlh9vqqj-hEeeu0xXdbba9frFj0-OqFfea0dXdd9 % vqai-hGuQ8kuc9pgc9q8qqaq-dir-f0-yqaiVgFr0xfr-xfr-xb9ad % baqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8qacaWGjb % Gaeyypa0Zaa8qCa8aabaWdbiGacshacaGGHbGaaiOBa8aadaahaaWc % beqaa8qacaaIYaaaaaWdaeaapeGaaGimaaWdaeaapeWaaSaaa8aaba % Wdbiabec8aWbWdaeaapeGaaGinaaaaa0Gaey4kIipakiaadIhacaqG % KbGaamiEaaaa!61F8! I = \int\limits_0^{\frac{\pi }{4}} {{{\tan }^2}} x{\rm{d}}x\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqr1ngB % PrgifHhDYfgasaacH8YjY-vipgYlh9vqqj-hEeeu0xXdbba9frFj0- % OqFfea0dXdd9vqai-hGuQ8kuc9pgc9q8qqaq-dir-f0-yqaiVgFr0x % fr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0 % deaaaaaaaaa8qadaWdXbWdaeaadaWcaaqaaiGacohacaGGPbGaaiOB % amaaCaaaleqabaGaaGOmaaaakiaadIhaaeaaciGGJbGaai4Baiaaco % hadaahaaWcbeqaaiaaikdaaaGccaWG4baaaiaabsgacaWG4baaleaa % peGaaGimaaWdaeaapeWaaSaaa8aabaWdbiabec8aWbWdaeaapeGaaG % inaaaaa0Gaey4kIipaaaa!4A6C! = \int\limits_0^{\frac{\pi }{4}} {\frac{{{{\sin }^2}x}}{{{{\cos }^2}x}}{\rm{d}}x} \)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqr1ngB % PrgifHhDYfgasaacH8YjY-vipgYlh9vqqj-hEeeu0xXdbba9frFj0- % OqFfea0dXdd9vqai-hGuQ8kuc9pgc9q8qqaq-dir-f0-yqaiVgFr0x % fr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0 % deaaaaaaaaa8qadaWdXbWdaeaadaWcaaqaaiaaigdacqGHsislciGG % JbGaai4BaiaacohadaahaaWcbeqaaiaaikdaaaGccaWG4baabaGaci % 4yaiaac+gacaGGZbWaaWbaaSqabeaacaaIYaaaaOGaamiEaaaacaqG % KbGaamiEaaWcbaWdbiaaicdaa8aabaWdbmaalaaapaqaa8qacqaHap % aCa8aabaWdbiaaisdaaaaaniabgUIiYdaaaa!4C10! = \int\limits_0^{\frac{\pi }{4}} {\frac{{1 - {{\cos }^2}x}}{{{{\cos }^2}x}}{\rm{d}}x} \)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqr1ngB % PrgifHhDYfgasaacH8YjY-vipgYlh9vqqj-hEeeu0xXdbba9frFj0- % OqFfea0dXdd9vqai-hGuQ8kuc9pgc9q8qqaq-dir-f0-yqaiVgFr0x % fr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0 % Zaa8qCaeaadaqadaqaamaalaaabaGaaGymaaqaaiGacogacaGGVbGa % ai4CamaaCaaaleqabaGaaGOmaaaakiaadIhaaaGaeyOeI0IaaGymaa % GaayjkaiaawMcaaiaabsgacaWG4baaleaacaaIWaaabaWaaSaaaeaa % cqaHapaCaeaacaaI0aaaaaqdcqGHRiI8aaaa!48F4! = \int\limits_0^{\frac{\pi }{4}} {\left( {\frac{1}{{{{\cos }^2}x}} - 1} \right){\rm{d}}x} \)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqr1ngB % PrgifHhDYfgasaacH8YjY-vipgYlh9vqqj-hEeeu0xXdbba9frFj0- % OqFfea0dXdd9vqai-hGuQ8kuc9pgc9q8qqaq-dir-f0-yqaiVgFr0x % fr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0 % ZaaqGaaeaadaqadaqaaiGacshacaGGHbGaaiOBaiaadIhacqGHsisl % caWG4baacaGLOaGaayzkaaaacaGLiWoadaqhaaWcbaGaaGimaaqaam % aalaaabaGaeqiWdahabaGaaGinaaaaaaaaaa!44ED! = \left. {\left( {\tan x - x} \right)} \right|_0^{\frac{\pi }{4}}\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqr1ngB % PrgifHhDYfgasaacH8YjY-vipgYlh9vqqj-hEeeu0xXdbba9frFj0- % OqFfea0dXdd9vqai-hGuQ8kuc9pgc9q8qqaq-dir-f0-yqaiVgFr0x % fr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0 % JaaGymaiabgkHiTmaalaaabaGaeqiWdahabaGaaGinaaaaaaa!3CD7! = 1 - \frac{\pi }{4}\)