what is the integral of xe^2x ?
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This should be soled as integrals by parts. In Integrals by parts it says if U and V are fuctions then,
`intUdv = UV-intVdu`
So let us take U= x and V=e^(2x)
Then by differentiation with respect to x;
dU/dx = 1
dU = dx
dV/dx = 2e^(2x)
dV = 2e^(2x) dx
By applying the intergration by parts;
`int(x*2e^(2x)) dx = x*e^(2x)-int(e^(2x)) dx`
`intx*e^(2x) dx =` (1/2)(`x*e^(2x)-int(e^(2x)) dx`)
So the answer is;
`int(x*e^(2x)) dx ` = ` (1/2)(x*e^(2x)-1/2*e^(2x))+C`
Where C is a contant.
Here is a similar problem being solved with integration by parts.
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