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

The integral from 0 to 2 of (2x+3)^3 is 290

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

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

290

Solution steps

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

Apply u-substitution

: \int_{3}^{7} \frac{u ^{3}}{2} d u

= \int_{3}^{7} \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}^{7} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{3}^{7}

= \frac{1}{2} [\frac{u ^{4}}{4}]_{3}^{7}

Compute the boundaries:

580

= \frac{1}{2} \cdot 580

Simplify

= 290

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What is the integral from 0 to 2 of (2x+3)^3 ?
The integral from 0 to 2 of (2x+3)^3 is 290