What is the integral from 1 to 2 of x*e^x ?

The integral from 1 to 2 of x*e^x is e^2

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integral from 1 to 2 of x*e^x

\int_{1}^{2} x \cdot e^{x} d x

e^{2}

Decimal

7.38905 \dots

Solution steps

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

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{1}^{2}

= [e^{x} x - \int e^{x} d x]_{1}^{2}

\int e^{x} d x = e^{x}

= [e^{x} x - e^{x}]_{1}^{2}

Compute the boundaries:

e^{2}

= e^{2}

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

\int_{1}^{3} 2 x d x

\int_{1}^{e} (x + \frac{1}{x}) d x

\int_{- 5}^{- 2} \frac{1}{( x + 3 ) ^{2}} d x

\int_{0}^{5} (- 2 x^{2} + 10 x) d x

What is the integral from 1 to 2 of x*e^x ?
The integral from 1 to 2 of x*e^x is e^2