What is the integral from 1 to 4 of (2x-1)^5 ?

The integral from 1 to 4 of (2x-1)^5 is 9804

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integral from 1 to 4 of (2x-1)^5

\int_{1}^{4} (2 x - 1)^{5} d x

9804

Solution steps

\int_{1}^{4} (2 x - 1)^{5} d x

Apply u-substitution

: \int_{1}^{7} \frac{u ^{5}}{2} d u

= \int_{1}^{7} \frac{u ^{5}}{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_{1}^{7} u^{5} d u

Apply the Power Rule

: [\frac{u ^{6}}{6}]_{1}^{7}

= \frac{1}{2} [\frac{u ^{6}}{6}]_{1}^{7}

Compute the boundaries:

19608

= \frac{1}{2} \cdot 19608

Simplify

= 9804

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What is the integral from 1 to 4 of (2x-1)^5 ?
The integral from 1 to 4 of (2x-1)^5 is 9804