What is the integral from 0 to 2 of x^2sqrt(x^3+5) ?

The integral from 0 to 2 of x^2sqrt(x^3+5) is (26sqrt(13)-10sqrt(5))/9

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integral from 0 to 2 of x^2sqrt(x^3+5)

\int_{0}^{2} x^{2} x^{3} + 5 d x

\frac{26 13 - 10 5}{9}

Decimal Notation

7.93151 \dots

Solution steps

\int_{0}^{2} x^{2} x^{3} + 5 d x

Apply u-substitution

: \int_{5}^{13} \frac{u}{3} d u

= \int_{5}^{13} \frac{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_{5}^{13} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{13}

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{13}

Compute the boundaries:

\frac{26 13 - 10 5}{3}

= \frac{1}{3} \cdot \frac{26 13 - 10 5}{3}

Simplify

= \frac{26 13 - 10 5}{9}

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What is the integral from 0 to 2 of x^2sqrt(x^3+5) ?
The integral from 0 to 2 of x^2sqrt(x^3+5) is (26sqrt(13)-10sqrt(5))/9