What is the integral from-3 to 5 of (4x+5)^3 ?

The integral from-3 to 5 of (4x+5)^3 is 24264

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integral from-3 to 5 of (4x+5)^3

\int_{- 3}^{5} (4 x + 5)^{3} d x

24264

Solution steps

\int_{- 3}^{5} (4 x + 5)^{3} d x

Apply u-substitution

: \int_{- 7}^{25} \frac{u ^{3}}{4} d u

= \int_{- 7}^{25} \frac{u ^{3}}{4} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int_{- 7}^{25} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{- 7}^{25}

= \frac{1}{4} [\frac{u ^{4}}{4}]_{- 7}^{25}

Compute the boundaries:

97056

= \frac{1}{4} \cdot 97056

Simplify

= 24264

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What is the integral from-3 to 5 of (4x+5)^3 ?
The integral from-3 to 5 of (4x+5)^3 is 24264