解决不定积分 急急急！

不定积分求解。急急急！！！要过程~

F'(x)F(x)=1/2xe^x²
∫F'(x)F(x)dx=∫1/2xe^x²dx
F²(x)/2=1/4e^(x²)+c
1/2=1/4+c
c=1/4
F²(x)=1/2e^x² +1/2
F(X)=√(1/2e^x² +1/2)
f(x)=F'(x)=[√(1/2e^x² +1/2)]'
自己求吧。

∫(3x+1)/(x^2+2x+17) dx
=(3/2)∫ (2x+2)/(x^2+2x+17) dx - 2∫ dx/(x^2+2x+17)
= (3/2)ln|x^2+2x+17| - 2∫ dx/(x^2+2x+17)

x^2+2x+17 = (x+1)^2 + 16
let
x+1= 4tany
dx = 4(secy)^2dy

∫ dx/(x^2+2x+17)
=(1/4)∫ dy
=(1/4)y+ C'
=(1/4)arctan[(x+1)/4] + C'

∫(3x+1)/(x^2+2x+17) dx
= (3/2)ln|x^2+2x+17| - 2∫ dx/(x^2+2x+17)
= (3/2)ln|x^2+2x+17| - (1/2)arctan[(x+1)/4] + C

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解决不定积分 急急急！视频