What is the integral from 2 to 4 of x^2e^{x^3+5} ?

The integral from 2 to 4 of x^2e^{x^3+5} is (e^{69}-e^{13})/3

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integral from 2 to 4 of x^2e^{x^3+5}

\int_{2}^{4} x^{2} e^{x^{3} + 5} d x

\frac{e ^{69} - e ^{13}}{3}

Solution steps

\int_{2}^{4} x^{2} e^{x^{3} + 5} d x

Apply u-substitution

: \int_{13}^{69} \frac{e ^{u}}{3} d u

= \int_{13}^{69} \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_{13}^{69} e^{u} d u

Use the common integral:

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

= \frac{1}{3} [e^{u}]_{13}^{69}

Compute the boundaries:

e^{69} - e^{13}

= \frac{1}{3} (e^{69} - e^{13})

Simplify

= \frac{e ^{69} - e ^{13}}{3}

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What is the integral from 2 to 4 of x^2e^{x^3+5} ?
The integral from 2 to 4 of x^2e^{x^3+5} is (e^{69}-e^{13})/3