Use integration by parts. integral of xe^xdx =xe^x-integral of e^xdx.
This is xe^x-e^x +C. Check by differentiating. We get x(e^x)+e^x(1)-e^x, which equals xe^x. That's it!
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If x has the power 2 then you want the integral of x2, I think. When you integrate this you get : x3/3 , plus a constant.
let u = x du=dx let dv= e^x v=e^x ∫ xe^(x)dx = xe^x - ∫ e^(x)dx = xe^x - e^x = e^x ( x-1 ) + c
xe^(5x) is an expression involving x and Euler's constant
-(10/x)
To integrate a function you find what the function you have is the derivative of. for example the derivative of x^2 is 2x. so the integral of 2x is x^2.