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

The integral from 2 to 3 of xe^{2x} is (5e^6-3e^4)/4

Popular >

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

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

\frac{5 e ^{6} - 3 e ^{4}}{4}

Decimal

463.33737 \dots

Solution steps

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

Apply u-substitution

: \int_{4}^{6} \frac{e ^{u} u}{4} d u

= \int_{4}^{6} \frac{e ^{u} u}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int_{4}^{6} e^{u} u d u

Apply Integration By Parts

: [e^{u} u - \int e^{u} d u]_{4}^{6}

= \frac{1}{4} [e^{u} u - \int e^{u} d u]_{4}^{6}

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

= \frac{1}{4} [e^{u} u - e^{u}]_{4}^{6}

Compute the boundaries:

5 e^{6} - 3 e^{4}

= \frac{1}{4} (5 e^{6} - 3 e^{4})

Simplify

= \frac{5 e ^{6} - 3 e ^{4}}{4}

\int_{0}^{5} \frac{10}{x} d x

\int_{0}^{1} (x + 5) (x - 6) d x

\int_{- π}^{π} sin^{2} (n x) d x

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

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

What is the integral from 2 to 3 of xe^{2x} ?
The integral from 2 to 3 of xe^{2x} is (5e^6-3e^4)/4