What is the integral from 2 to 5 of (10x+12)^3 ?

The integral from 2 to 5 of (10x+12)^3 is 343194

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integral from 2 to 5 of (10x+12)^3

\int_{2}^{5} (10 x + 12)^{3} d x

343194

Solution steps

\int_{2}^{5} (10 x + 12)^{3} d x

Apply u-substitution

: \int_{32}^{62} \frac{u ^{3}}{10} d u

= \int_{32}^{62} \frac{u ^{3}}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int_{32}^{62} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{32}^{62}

= \frac{1}{10} [\frac{u ^{4}}{4}]_{32}^{62}

Compute the boundaries:

3431940

= \frac{1}{10} \cdot 3431940

Simplify

= 343194

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What is the integral from 2 to 5 of (10x+12)^3 ?
The integral from 2 to 5 of (10x+12)^3 is 343194