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

The integral from 0 to 2 of x^2(1+2x^3)^3 is 3480

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

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

3480

Solution steps

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

Apply u-substitution

: \int_{1}^{17} \frac{u ^{3}}{6} d u

= \int_{1}^{17} \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}^{17} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{1}^{17}

= \frac{1}{6} [\frac{u ^{4}}{4}]_{1}^{17}

Compute the boundaries:

20880

= \frac{1}{6} \cdot 20880

Simplify

= 3480

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\frac{d}{d x} (1 - \frac{2}{x})

What is the integral from 0 to 2 of x^2(1+2x^3)^3 ?
The integral from 0 to 2 of x^2(1+2x^3)^3 is 3480