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

The integral from 2 to 3 of e^{x^3}x^2 is (e^{27}-e^8)/3

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

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

\frac{e ^{27} - e ^{8}}{3}

Decimal

177349412540.27994

Solution steps

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

Apply u-substitution

: \int_{8}^{27} \frac{e ^{u}}{3} d u

= \int_{8}^{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

= \frac{1}{3} \cdot \int_{8}^{27} e^{u} d u

Use the common integral:

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

= \frac{1}{3} [e^{u}]_{8}^{27}

Compute the boundaries:

e^{27} - e^{8}

= \frac{1}{3} (e^{27} - e^{8})

Simplify

= \frac{e ^{27} - e ^{8}}{3}

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What is the integral from 2 to 3 of e^{x^3}x^2 ?
The integral from 2 to 3 of e^{x^3}x^2 is (e^{27}-e^8)/3