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

The integral from 0 to 1 of (1+5x)^3 is 259/4

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

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

\frac{259}{4}

Decimal

64.75

Solution steps

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

Apply u-substitution

: \int_{1}^{6} \frac{u ^{3}}{5} d u

= \int_{1}^{6} \frac{u ^{3}}{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_{1}^{6} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{1}^{6}

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

Compute the boundaries:

\frac{1295}{4}

= \frac{1}{5} \cdot \frac{1295}{4}

Simplify

= \frac{259}{4}

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What is the integral from 0 to 1 of (1+5x)^3 ?
The integral from 0 to 1 of (1+5x)^3 is 259/4