What is the integral from 0 to 1 of (2x+3)^{10} ?

The integral from 0 to 1 of (2x+3)^{10} is 24325489/11

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integral from 0 to 1 of (2x+3)^{10}

\int_{0}^{1} (2 x + 3)^{10} d x

\frac{24325489}{11}

Decimal

2211408.09090 \dots

Solution steps

\int_{0}^{1} (2 x + 3)^{10} d x

Apply u-substitution

= \int_{3}^{5} \frac{u ^{10}}{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_{3}^{5} u^{10} d u

Apply the Power Rule

= \frac{1}{2} [\frac{u ^{11}}{11}]_{3}^{5}

Compute the boundaries:

\frac{48650978}{11}

= \frac{1}{2} \cdot \frac{48650978}{11}

Simplify

= \frac{24325489}{11}

What is the integral from 0 to 1 of (2x+3)^{10} ?
The integral from 0 to 1 of (2x+3)^{10} is 24325489/11