What is the integral from 1 to 3 of x^4sqrt(x^5-1) ?

The integral from 1 to 3 of x^4sqrt(x^5-1) is (5324sqrt(2))/(15)

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integral from 1 to 3 of x^4sqrt(x^5-1)

\int_{1}^{3} x^{4} x^{5} - 1 d x

\frac{5324 2}{15}

Decimal Notation

501.95153 \dots

Solution steps

\int_{1}^{3} x^{4} x^{5} - 1 d x

Apply u-substitution

: \int_{0}^{242} \frac{u}{5} d u

= \int_{0}^{242} \frac{u}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{0}^{242} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{242}

= \frac{1}{5} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{242}

Compute the boundaries:

\frac{5324 2}{3}

= \frac{1}{5} \cdot \frac{5324 2}{3}

Simplify

= \frac{5324 2}{15}

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What is the integral from 1 to 3 of x^4sqrt(x^5-1) ?
The integral from 1 to 3 of x^4sqrt(x^5-1) is (5324sqrt(2))/(15)