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

The integral from-1 to 3 of (5x+1)^5 is 559104

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

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

559104

Solution steps

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

Apply u-substitution

: \int_{- 4}^{16} \frac{u ^{5}}{5} d u

= \int_{- 4}^{16} \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_{- 4}^{16} u^{5} d u

Apply the Power Rule

: [\frac{u ^{6}}{6}]_{- 4}^{16}

= \frac{1}{5} [\frac{u ^{6}}{6}]_{- 4}^{16}

Compute the boundaries:

2795520

= \frac{1}{5} \cdot 2795520

Simplify

= 559104

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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 559104