What is the integral from 0 to 5 of xe^{x^2} ?

The integral from 0 to 5 of xe^{x^2} is (e^{25}-1)/2

Popular >

integral from 0 to 5 of xe^{x^2}

\int_{0}^{5} x e^{x^{2}} d x

\frac{e ^{25} - 1}{2}

Decimal

36002449668.19289

Solution steps

\int_{0}^{5} x e^{x^{2}} d x

Apply u-substitution

: \int_{0}^{25} \frac{e ^{u}}{2} d u

= \int_{0}^{25} \frac{e ^{u}}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{25} e^{u} d u

Use the common integral:

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

= \frac{1}{2} [e^{u}]_{0}^{25}

Compute the boundaries:

e^{25} - 1

= \frac{1}{2} (e^{25} - 1)

Simplify

= \frac{e ^{25} - 1}{2}

\int_{\frac{3}{2}}^{2} 5 t cos (π t) d t

\int_{0}^{1} 3 x (x^{2} - 1)^{3} d x

\int_{0}^{4} π (y + 3)^{2} d y

\int_{0}^{6} x^{2} + 2 d x

\int_{0}^{1} x^{2} + 2 x - 3 d x

What is the integral from 0 to 5 of xe^{x^2} ?
The integral from 0 to 5 of xe^{x^2} is (e^{25}-1)/2