What is the integral from 3 to 5 of xe^{x^2} ?

The integral from 3 to 5 of xe^{x^2} is (e^{25}-e^9)/2

Popular >

integral from 3 to 5 of xe^{x^2}

\int_{3}^{5} x e^{x^{2}} d x

\frac{e ^{25} - e ^{9}}{2}

Decimal

36002445617.150925

Solution steps

\int_{3}^{5} x e^{x^{2}} d x

Apply u-substitution

: \int_{9}^{25} \frac{e ^{u}}{2} d u

= \int_{9}^{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_{9}^{25} e^{u} d u

Use the common integral:

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

= \frac{1}{2} [e^{u}]_{9}^{25}

Compute the boundaries:

e^{25} - e^{9}

= \frac{1}{2} (e^{25} - e^{9})

Simplify

= \frac{e ^{25} - e ^{9}}{2}

\int_{1}^{3} (\frac{3 x ^{2} + 4 x + 1}{x}) d x

\int_{0}^{1} t 9 t^{2} + 16 d t

\int_{- 5}^{3} x^{2} + 2 x - 15 d x

\int_{0}^{2} (3 t - 1)^{60} d t

\int_{0}^{4 - y^{2}} z (- y + 2) d z

What is the integral from 3 to 5 of xe^{x^2} ?
The integral from 3 to 5 of xe^{x^2} is (e^{25}-e^9)/2