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

The integral from-1 to 2 of x^2(4+x^3)^5 is 331695/2

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

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

\frac{331695}{2}

Decimal Notation

165847.5

Solution steps

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

Apply u-substitution

: \int_{3}^{12} \frac{u ^{5}}{3} d u

= \int_{3}^{12} \frac{u ^{5}}{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_{3}^{12} u^{5} d u

Apply the Power Rule

: [\frac{u ^{6}}{6}]_{3}^{12}

= \frac{1}{3} [\frac{u ^{6}}{6}]_{3}^{12}

Compute the boundaries:

\frac{995085}{2}

= \frac{1}{3} \cdot \frac{995085}{2}

Simplify

= \frac{331695}{2}

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What is the integral from-1 to 2 of x^2(4+x^3)^5 ?
The integral from-1 to 2 of x^2(4+x^3)^5 is 331695/2