∫(sec t)³dt
=∫(1/cos t)³dt
=∫(1/cos t)^4 * cos t dt
=∫1/(1-sin²t)² d sin t
=∫1/(1-sint)²(1+sint)² d sin t
=1/4 * ∫[1/(1-sin t) + 1/(1+sint)]² d sin t
=1/4∫[1/(1-sint)²+1/(1+sint)²+2/(1-sint)(1+sint)] d sin t
=1/4[1/(1-sint) - 1/(1+sint) - ln (1-sint) + ln (1+sint)] + C
=2tg t sec t + 1/4 ln (1+sint)/(1-sint) + C
希望我的回答能够帮助到您。
