What is the integral from 0 to 1 of xe^{x^2}-x ?

The integral from 0 to 1 of xe^{x^2}-x is (e-1)/2-1/2

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integral from 0 to 1 of xe^{x^2}-x

\int_{0}^{1} x e^{x^{2}} - x d x

\frac{e - 1}{2} - \frac{1}{2}

Decimal

0.35914 \dots

Solution steps

\int_{0}^{1} x e^{x^{2}} - x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} x e^{x^{2}} d x - \int_{0}^{1} x d x

\int_{0}^{1} x e^{x^{2}} d x = \frac{e - 1}{2}

\int_{0}^{1} x d x = \frac{1}{2}

= \frac{e - 1}{2} - \frac{1}{2}

What is the integral from 0 to 1 of xe^{x^2}-x ?
The integral from 0 to 1 of xe^{x^2}-x is (e-1)/2-1/2