What is the integral from 0 to 1 of (3x+5)^6 ?

The integral from 0 to 1 of (3x+5)^6 is 673009/7

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integral from 0 to 1 of (3x+5)^6

\int_{0}^{1} (3 x + 5)^{6} d x

\frac{673009}{7}

Decimal

96144.14285 \dots

Solution steps

\int_{0}^{1} (3 x + 5)^{6} d x

Apply u-substitution

: \int_{5}^{8} \frac{u ^{6}}{3} d u

= \int_{5}^{8} \frac{u ^{6}}{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_{5}^{8} u^{6} d u

Apply the Power Rule

: [\frac{u ^{7}}{7}]_{5}^{8}

= \frac{1}{3} [\frac{u ^{7}}{7}]_{5}^{8}

Compute the boundaries:

\frac{2019027}{7}

= \frac{1}{3} \cdot \frac{2019027}{7}

Simplify

= \frac{673009}{7}

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What is the integral from 0 to 1 of (3x+5)^6 ?
The integral from 0 to 1 of (3x+5)^6 is 673009/7