How do you use substitution to integrate $(x+4)e^(x^(2)+8x+17)$ ?

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Answer 1 · 2015-06-20T12:48:20

The answer is: $F(x)=1/2e^(x^2+8x+17) +C$

$int((x+4)e^(x^2+8x+17))dx=|(x^2+8x+17=t),((2x+8)dx=dt),((x+4)dx=dt/2)|$
$= int(e^t)dt/2=1/2int e^tdt=1/2e^t+C=1/2e^(x^2+8x+17) +C$

How do you use substitution to integrate (x+4)e^(x^(2)+8x+17)(x+4)e^(x^(2)+8x+17)?