微积分数学问题求解答，求详细步骤 微积分数学问题求解答
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\u222b tant*sec³t dt
=\u222b sint /(cost)^4 dt
=- \u222b (cost)^(-4) d(cost)
=(1/3) *(cost)^(-3)+C
=1/(3cos³t)+C
38)
\u222b tanx*(secx)^5 dx
=\u222b sinx / (cosx)^6 dx
=- \u222b (cosx)^(-6) d(cosx)
= (1/5)*(cosx)^(-5)+C
=1/[5(cosx)^5 ]+C
(1/2)sin^2-(1/4)sin^4
=(1/4)*sin^2*(2-sin^2)
=(1/4)sin^2+(1/4)sin^2cos^2
=(1/4)sin^2+(1/4)cos^2-(1/4)cos^4
(1/4)-(1/4)cos^4
因为C代表任意数，所以(1/4)可以归并入C，所以你的答案和书上的是等价的。
此题可以这么做
-∫cos^3dcos=-(1/4)cos^4+C
答：凑微分做出来的
∫ cos³xsinx dx
= - ∫ cos³x d(cosx)
=- (1/4)*(cosx)^4+C
都没错
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