Evaluate `int x e^(x^2)dx` :
Let `u=x^2 ` so du=2xdx. Then:
`int x e^(x^2)dx=1/2int e^u du `
`=1/2e^u +C `
Substituting back for u we get:
`int xe^(x^2)dx=1/2e^(x^2)+C `
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We can check by taking the derivative:
`d/(dx)[1/2e^(x^2)+C]=(1/2)(e^(x^2))(2x)=xe^(x^2) ` as required.
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