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

The integral from 2 to 3 of (x+1)(x^2+2x)^3 is 46529/8

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

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

\frac{46529}{8}

Decimal

5816.125

Solution steps

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

Apply u-substitution

= \int_{8}^{15} \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_{8}^{15} u^{3} d u

Apply the Power Rule

= \frac{1}{2} [\frac{u ^{4}}{4}]_{8}^{15}

Compute the boundaries:

\frac{46529}{4}

= \frac{1}{2} \cdot \frac{46529}{4}

Simplify

= \frac{46529}{8}

What is the integral from 2 to 3 of (x+1)(x^2+2x)^3 ?
The integral from 2 to 3 of (x+1)(x^2+2x)^3 is 46529/8