What is the integral from 1 to 2 of (3+5x)^3 ?

The integral from 1 to 2 of (3+5x)^3 is 4893/4

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integral from 1 to 2 of (3+5x)^3

\int_{1}^{2} (3 + 5 x)^{3} d x

\frac{4893}{4}

Decimal Notation

1223.25

Solution steps

\int_{1}^{2} (3 + 5 x)^{3} d x

Apply u-substitution

: \int_{8}^{13} \frac{u ^{3}}{5} d u

= \int_{8}^{13} \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_{8}^{13} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{8}^{13}

= \frac{1}{5} [\frac{u ^{4}}{4}]_{8}^{13}

Compute the boundaries:

\frac{24465}{4}

= \frac{1}{5} \cdot \frac{24465}{4}

Simplify

= \frac{4893}{4}

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What is the integral from 1 to 2 of (3+5x)^3 ?
The integral from 1 to 2 of (3+5x)^3 is 4893/4