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

The integral from 1 to 2 of (x+1)(x^2+2x)^3 is 4015/8

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integral from 1 to 2 of (x+1)(x^2+2x)^3

\int_{1}^{2} (x + 1) (x^{2} + 2 x)^{3} d x

\frac{4015}{8}

Decimal

501.875

Solution steps

\int_{1}^{2} (x + 1) (x^{2} + 2 x)^{3} d x

Apply u-substitution

: \int_{3}^{8} \frac{u ^{3}}{2} d u

= \int_{3}^{8} \frac{u ^{3}}{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_{3}^{8} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{3}^{8}

= \frac{1}{2} [\frac{u ^{4}}{4}]_{3}^{8}

Compute the boundaries:

\frac{4015}{4}

= \frac{1}{2} \cdot \frac{4015}{4}

Simplify

= \frac{4015}{8}

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What is the integral from 1 to 2 of (x+1)(x^2+2x)^3 ?
The integral from 1 to 2 of (x+1)(x^2+2x)^3 is 4015/8