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

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1 Answer

Jan 29, 2015

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

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