What is the integral of $f (x) = x e^{2 x}$ $f(x)=xe^(2x)$ ?

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Answer 1 · 2015-01-29T19:56:31

I would use integration by parts:
Where you have:
$intf(x)*g(x)dx=F(x)*g(x)-intF(x)*g'(x)dx$

Where:
$F(x)=intf(x)dx$
$g'(x)$ is the derivative of $g(x)$

In your case you can choose:
$f(x)=e^(2x)$
$g(x)=x$

$intxe^(2x)dx=xe^(2x)/2-int1*e^(2x)/2dx=$
$=xe^(2x)/2-e^(2x)/4+c$

Hope it helps

What is the integral of f(x)=xe^(2x)f(x)=xe2xf(x)=xe^(2x)?