What is the integral from 2 to 6 of (x+1)(x^2+2x)^2 ?

The integral from 2 to 6 of (x+1)(x^2+2x)^2 is 55040/3

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integral from 2 to 6 of (x+1)(x^2+2x)^2

\int_{2}^{6} (x + 1) (x^{2} + 2 x)^{2} d x

\frac{55040}{3}

Decimal

18346.66666 \dots

Solution steps

\int_{2}^{6} (x + 1) (x^{2} + 2 x)^{2} d x

Apply u-substitution

: \int_{8}^{48} \frac{u ^{2}}{2} d u

= \int_{8}^{48} \frac{u ^{2}}{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_{8}^{48} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{8}^{48}

= \frac{1}{2} [\frac{u ^{3}}{3}]_{8}^{48}

Compute the boundaries:

\frac{110080}{3}

= \frac{1}{2} \cdot \frac{110080}{3}

Simplify

= \frac{55040}{3}

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What is the integral from 2 to 6 of (x+1)(x^2+2x)^2 ?
The integral from 2 to 6 of (x+1)(x^2+2x)^2 is 55040/3