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

The integral from 1 to 2 of x^2(x^3+5)^4 is 363517/15

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integral from 1 to 2 of x^2(x^3+5)^4

\int_{1}^{2} x^{2} (x^{3} + 5)^{4} d x

\frac{363517}{15}

Decimal

24234.46666 \dots

Solution steps

\int_{1}^{2} x^{2} (x^{3} + 5)^{4} d x

Apply u-substitution

= \int_{6}^{13} \frac{u ^{4}}{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_{6}^{13} u^{4} d u

Apply the Power Rule

= \frac{1}{3} [\frac{u ^{5}}{5}]_{6}^{13}

Compute the boundaries:

\frac{363517}{5}

= \frac{1}{3} \cdot \frac{363517}{5}

Simplify

= \frac{363517}{15}

What is the integral from 1 to 2 of x^2(x^3+5)^4 ?
The integral from 1 to 2 of x^2(x^3+5)^4 is 363517/15