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

The integral from 0 to 1 of x^2(2+2x^3)^3 is 10

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

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

10

Solution steps

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

Apply u-substitution

: \int_{2}^{4} \frac{u ^{3}}{6} d u

= \int_{2}^{4} \frac{u ^{3}}{6} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{6} \cdot \int_{2}^{4} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{2}^{4}

= \frac{1}{6} [\frac{u ^{4}}{4}]_{2}^{4}

Compute the boundaries:

60

= \frac{1}{6} \cdot 60

Simplify

= 10

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\int_{a}^{b} \frac{1}{( x - a ) ^{n}} d x

\int_{- π}^{π} sin^{6} (x) d x

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