What is the integral from 1 to 5 of (3x-5)^4 ?

The integral from 1 to 5 of (3x-5)^4 is 33344/5

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integral from 1 to 5 of (3x-5)^4

\int_{1}^{5} (3 x - 5)^{4} d x

\frac{33344}{5}

Decimal

6668.8

Solution steps

\int_{1}^{5} (3 x - 5)^{4} d x

Apply u-substitution

= \int_{- 2}^{10} \frac{u ^{4}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{- 2}^{10} u^{4} d u

Apply the Power Rule

= \frac{1}{3} [\frac{u ^{5}}{5}]_{- 2}^{10}

Compute the boundaries:

\frac{100032}{5}

= \frac{1}{3} \cdot \frac{100032}{5}

Simplify

= \frac{33344}{5}

What is the integral from 1 to 5 of (3x-5)^4 ?
The integral from 1 to 5 of (3x-5)^4 is 33344/5