What is the integral from 0 to 1 of x^2(2+2x^3)^5 ?

The integral from 0 to 1 of x^2(2+2x^3)^5 is 112

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integral from 0 to 1 of x^2(2+2x^3)^5

\int_{0}^{1} x^{2} (2 + 2 x^{3})^{5} d x

112

Solution steps

\int_{0}^{1} x^{2} (2 + 2 x^{3})^{5} d x

Apply u-substitution

: \int_{2}^{4} \frac{u ^{5}}{6} d u

= \int_{2}^{4} \frac{u ^{5}}{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^{5} d u

Apply the Power Rule

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

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

Compute the boundaries:

672

= \frac{1}{6} \cdot 672

Simplify

= 112

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\int_{2}^{x} \frac{1}{ln ( t )} d t

\int_{0}^{1} 3 cos (\frac{π x}{2}) d x

What is the integral from 0 to 1 of x^2(2+2x^3)^5 ?
The integral from 0 to 1 of x^2(2+2x^3)^5 is 112