What is the integral from 0 to 1 of xe^{4x^2+3} ?

The integral from 0 to 1 of xe^{4x^2+3} is (e^7-e^3)/8

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integral from 0 to 1 of xe^{4x^2+3}

\int_{0}^{1} x e^{4 x^{2} + 3} d x

\frac{e ^{7} - e ^{3}}{8}

Decimal Notation

134.56845 \dots

Solution steps

\int_{0}^{1} x e^{4 x^{2} + 3} d x

Apply u-substitution

: \int_{3}^{7} \frac{e ^{u}}{8} d u

= \int_{3}^{7} \frac{e ^{u}}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int_{3}^{7} e^{u} d u

Use the common integral:

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

= \frac{1}{8} [e^{u}]_{3}^{7}

Compute the boundaries:

e^{7} - e^{3}

= \frac{1}{8} (e^{7} - e^{3})

Simplify

= \frac{e ^{7} - e ^{3}}{8}

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What is the integral from 0 to 1 of xe^{4x^2+3} ?
The integral from 0 to 1 of xe^{4x^2+3} is (e^7-e^3)/8