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

1 Answer

Daniel L. · Jim H

Jun 20, 2015

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#

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