What is the integral from 0 to 4 of (2x+1)^3 ?

The integral from 0 to 4 of (2x+1)^3 is 820

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integral from 0 to 4 of (2x+1)^3

\int_{0}^{4} (2 x + 1)^{3} d x

820

Solution steps

\int_{0}^{4} (2 x + 1)^{3} d x

Apply u-substitution

: \int_{1}^{9} \frac{u ^{3}}{2} d u

= \int_{1}^{9} \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_{1}^{9} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{1}^{9}

= \frac{1}{2} [\frac{u ^{4}}{4}]_{1}^{9}

Compute the boundaries:

1640

= \frac{1}{2} \cdot 1640

Simplify

= 820

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What is the integral from 0 to 4 of (2x+1)^3 ?
The integral from 0 to 4 of (2x+1)^3 is 820