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

The integral from 1 to 2 of x(x^2+1)^5 is 5187/4

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

\int_{1}^{2} x (x^{2} + 1)^{5} d x

\frac{5187}{4}

Decimal

1296.75

Solution steps

\int_{1}^{2} x (x^{2} + 1)^{5} d x

Apply u-substitution

: \int_{2}^{5} \frac{u ^{5}}{2} d u

= \int_{2}^{5} \frac{u ^{5}}{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_{2}^{5} u^{5} d u

Apply the Power Rule

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

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

Compute the boundaries:

\frac{5187}{2}

= \frac{1}{2} \cdot \frac{5187}{2}

Simplify

= \frac{5187}{4}

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What is the integral from 1 to 2 of x(x^2+1)^5 ?
The integral from 1 to 2 of x(x^2+1)^5 is 5187/4