What is the integral from 1 to 2 of x(x^2-1)^4 ?

The integral from 1 to 2 of x(x^2-1)^4 is 243/10

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integral from 1 to 2 of x(x^2-1)^4

\int_{1}^{2} x (x^{2} - 1)^{4} d x

\frac{243}{10}

Decimal

24.3

Solution steps

\int_{1}^{2} x (x^{2} - 1)^{4} d x

Apply u-substitution

= \int_{0}^{3} \frac{u ^{4}}{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^{4} d u

Apply the Power Rule

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

Compute the boundaries:

\frac{243}{5}

= \frac{1}{2} \cdot \frac{243}{5}

Simplify

= \frac{243}{10}

What is the integral from 1 to 2 of x(x^2-1)^4 ?
The integral from 1 to 2 of x(x^2-1)^4 is 243/10