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

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

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

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

\frac{10}{3}

Decimal Notation

3.33333 \dots

Solution steps

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

Apply u-substitution

: \int_{1}^{3} \frac{u ^{3}}{6} d u

= \int_{1}^{3} \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_{1}^{3} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{1}^{3}

= \frac{1}{6} [\frac{u ^{4}}{4}]_{1}^{3}

Compute the boundaries:

20

= \frac{1}{6} \cdot 20

Simplify

= \frac{10}{3}

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