What is the integral from 1 to 2 of x(x^2-1)^7 ?

The integral from 1 to 2 of x(x^2-1)^7 is 6561/16

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integral from 1 to 2 of x(x^2-1)^7

\int_{1}^{2} x (x^{2} - 1)^{7} d x

\frac{6561}{16}

Decimal Notation

410.0625

Solution steps

\int_{1}^{2} x (x^{2} - 1)^{7} d x

Apply u-substitution

: \int_{0}^{3} \frac{u ^{7}}{2} d u

= \int_{0}^{3} \frac{u ^{7}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{3} u^{7} d u

Apply the Power Rule

: [\frac{u ^{8}}{8}]_{0}^{3}

= \frac{1}{2} [\frac{u ^{8}}{8}]_{0}^{3}

Compute the boundaries:

\frac{6561}{8}

= \frac{1}{2} \cdot \frac{6561}{8}

Simplify

= \frac{6561}{16}

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What is the integral from 1 to 2 of x(x^2-1)^7 ?
The integral from 1 to 2 of x(x^2-1)^7 is 6561/16