What is the integral from 1 to 5 of (2x-5)^3 ?

The integral from 1 to 5 of (2x-5)^3 is 68

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integral from 1 to 5 of (2x-5)^3

\int_{1}^{5} (2 x - 5)^{3} d x

68

Solution steps

\int_{1}^{5} (2 x - 5)^{3} d x

Apply u-substitution

= \int_{- 3}^{5} \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}^{5} u^{3} d u

Apply the Power Rule

= \frac{1}{2} [\frac{u ^{4}}{4}]_{- 3}^{5}

Compute the boundaries:

136

= \frac{1}{2} \cdot 136

Simplify

= 68

What is the integral from 1 to 5 of (2x-5)^3 ?
The integral from 1 to 5 of (2x-5)^3 is 68