What is the integral from 1 to 3 of 2x^2e^{x^3} ?

The integral from 1 to 3 of 2x^2e^{x^3} is (2(e^{27}-e))/3

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integral from 1 to 3 of 2x^2e^{x^3}

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

\frac{2 ( e ^{27} - e )}{3}

Decimal Notation

354698827066

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{1}^{3} x^{2} e^{x^{3}} d x

Apply u-substitution

: \int_{1}^{27} \frac{e ^{u}}{3} d u

= 2 \cdot \int_{1}^{27} \frac{e ^{u}}{3} d u

Take the constant out:

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

= 2 \cdot \frac{1}{3} \cdot \int_{1}^{27} e^{u} d u

Use the common integral:

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

= 2 \cdot \frac{1}{3} [e^{u}]_{1}^{27}

Simplify

2 \cdot \frac{1}{3} [e^{u}]_{1}^{27} : \frac{2}{3} [e^{u}]_{1}^{27}

= \frac{2}{3} [e^{u}]_{1}^{27}

Compute the boundaries:

e^{27} - e

= \frac{2}{3} (e^{27} - e)

Simplify

= \frac{2 ( e ^{27} - e )}{3}

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What is the integral from 1 to 3 of 2x^2e^{x^3} ?
The integral from 1 to 3 of 2x^2e^{x^3} is (2(e^{27}-e))/3