上课不好好听课的孩子有不定积分不会做帮帮忙
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发布时间：2022-07-21 15:11
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热心网友
时间：2023-10-30 08:31
sec(x)tan(x)
MANUALLY" COMPUTED ANTIDERIVATIVE:
Problem:
∫sin(x)cos2(x)dx∫sin(x)cos2(x)dx
Substitute u=cos(x)u=cos(x) ⟶⟶ dx=−1sin(x)dx=−1sin(x) (Steps):
=−∫1u2=−∫1u2
Now solving:
∫1u2∫1u2
Apply power rule:
∫un=un+1n+1∫un=un+1n+1 with n=−2n=−2:
=−1u=−1u
Plug in solved integrals:
−∫1u2−∫1u2
=1u=1u
Undo substitution u=cos(x)u=cos(x):
=1cos(x)=1cos(x)
The problem is solved:
∫sin(x)cos2(x)dx∫sin(x)cos2(x)dx
=1cos(x)+C=1cos(x)+C
Rewrite/simplify:
=sec(x)+C
ANTIDERIVATIVE COMPUTED BY MAXIMA:
1cos(x)+C
