Int of xe^x^2dx

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.