What is the integral from 1 to 5 of (9x)^3 ?

The integral from 1 to 5 of (9x)^3 is 113724

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integral from 1 to 5 of (9x)^3

\int_{1}^{5} (9 x)^{3} d x

113724

Solution steps

\int_{1}^{5} (9 x)^{3} d x

Simplify

(9 x)^{3} : 729 x^{3}

= \int_{1}^{5} 729 x^{3} d x

Take the constant out:

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

= 729 \cdot \int_{1}^{5} x^{3} d x

Apply the Power Rule

= 729 [\frac{x ^{4}}{4}]_{1}^{5}

Compute the boundaries:

156

= 729 \cdot 156

Simplify

= 113724

What is the integral from 1 to 5 of (9x)^3 ?
The integral from 1 to 5 of (9x)^3 is 113724