What is the integral from 2 to 4 of xe^{4x} ?

The integral from 2 to 4 of xe^{4x} is (15e^{16}-7e^8)/(16)

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integral from 2 to 4 of xe^{4x}

\int_{2}^{4} x e^{4 x} d x

\frac{15 e ^{16} - 7 e ^{8}}{16}

Decimal

8329424.44385 \dots

Solution steps

\int_{2}^{4} x e^{4 x} d x

Apply u-substitution

: \int_{8}^{16} \frac{e ^{u} u}{16} d u

= \int_{8}^{16} \frac{e ^{u} u}{16} d u

Take the constant out:

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

= \frac{1}{16} \cdot \int_{8}^{16} e^{u} u d u

Apply Integration By Parts

: [e^{u} u - \int e^{u} d u]_{8}^{16}

= \frac{1}{16} [e^{u} u - \int e^{u} d u]_{8}^{16}

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

= \frac{1}{16} [e^{u} u - e^{u}]_{8}^{16}

Compute the boundaries:

15 e^{16} - 7 e^{8}

= \frac{1}{16} (15 e^{16} - 7 e^{8})

Simplify

= \frac{15 e ^{16} - 7 e ^{8}}{16}

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What is the integral from 2 to 4 of xe^{4x} ?
The integral from 2 to 4 of xe^{4x} is (15e^{16}-7e^8)/(16)