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

The integral from-1 to 3 of (5x-1)^5 is 748288/3

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

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

\frac{748288}{3}

Decimal Notation

249429.33333 \dots

Solution steps

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

Apply u-substitution

: \int_{- 6}^{14} \frac{u ^{5}}{5} d u

= \int_{- 6}^{14} \frac{u ^{5}}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{- 6}^{14} u^{5} d u

Apply the Power Rule

: [\frac{u ^{6}}{6}]_{- 6}^{14}

= \frac{1}{5} [\frac{u ^{6}}{6}]_{- 6}^{14}

Compute the boundaries:

\frac{3741440}{3}

= \frac{1}{5} \cdot \frac{3741440}{3}

Simplify

= \frac{748288}{3}

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What is the integral from-1 to 3 of (5x-1)^5 ?
The integral from-1 to 3 of (5x-1)^5 is 748288/3