Question

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

Answer 1

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

Explanation:

`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`