用凑微分法解答

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用凑微分法解答
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用凑微分法解答
用凑微分法解答
 

 

 

用凑微分法解答
(1):∫x^2(1+x^3)^(1/3)dx=1/3*∫(1+x^3)^(1/3)d(x^3+1)=1/4*(x^3+1)^(4/3)+c
(2):∫sinx*(cosx)^(-3/2)dx=-∫(cosx)^(-3/2)dcosx=2*(cosx)^(-1/2)+c
(3):∫sinxcosx/[1+(sinx)^4]dx=∫sinx/[1+(sinx)^4]dsinx=1/2*∫1/[1+(sinx)^4]d(sinx)^2
=1/2*arctan[(sinx)^2]+c