What is the integral from 1 to 3 of x^5sqrt(x^6-1) ?

The integral from 1 to 3 of x^5sqrt(x^6-1) is (1456sqrt(182))/9

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integral from 1 to 3 of x^5sqrt(x^6-1)

\int_{1}^{3} x^{5} x^{6} - 1 d x

\frac{1456 182}{9}

Decimal Notation

2182.50154 \dots

Solution steps

\int_{1}^{3} x^{5} x^{6} - 1 d x

Apply u-substitution

: \int_{0}^{728} \frac{u}{6} d u

= \int_{0}^{728} \frac{u}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int_{0}^{728} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{728}

= \frac{1}{6} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{728}

Compute the boundaries:

\frac{2912 182}{3}

= \frac{1}{6} \cdot \frac{2912 182}{3}

Simplify

= \frac{1456 182}{9}

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What is the integral from 1 to 3 of x^5sqrt(x^6-1) ?
The integral from 1 to 3 of x^5sqrt(x^6-1) is (1456sqrt(182))/9