What is the integral from 0 to 1 of x^2sqrt(5+x^3) ?

The integral from 0 to 1 of x^2sqrt(5+x^3) is (12sqrt(6)-10sqrt(5))/9

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integral from 0 to 1 of x^2sqrt(5+x^3)

\int_{0}^{1} x^{2} 5 + x^{3} d x

\frac{12 6 - 10 5}{9}

Decimal Notation

0.78146 \dots

Solution steps

\int_{0}^{1} x^{2} 5 + x^{3} d x

Apply u-substitution

: \int_{5}^{6} \frac{u}{3} d u

= \int_{5}^{6} \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}^{6} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{6}

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{6}

Compute the boundaries:

46 - \frac{10 5}{3}

= \frac{1}{3} (46 - \frac{10 5}{3})

Simplify

= \frac{12 6 - 10 5}{9}

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What is the integral from 0 to 1 of x^2sqrt(5+x^3) ?
The integral from 0 to 1 of x^2sqrt(5+x^3) is (12sqrt(6)-10sqrt(5))/9