How do you integrate e^2xcosx dxe2xcosxdx?

1 Answer
Gió
Feb 7, 2015

Starting from:
inte^2xcos(x)dx=∫e2xcos(x)dx= I would take the constant e^2e2 out of the integral:
e^2intxcos(x)dx=e2∫xcos(x)dx= then 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 choosing g(x)=x you get:

e^2[x*sin(x)-intsin(x)*1dx]=
e^2[xsin(x)+cos(x)]+c

hope it helps

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