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

The integral from 2 to 3 of x^2(1+2x^3)^3 is 377796

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

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

377796

Solution steps

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

Apply u-substitution

: \int_{17}^{55} \frac{u ^{3}}{6} d u

= \int_{17}^{55} \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_{17}^{55} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{17}^{55}

= \frac{1}{6} [\frac{u ^{4}}{4}]_{17}^{55}

Compute the boundaries:

2266776

= \frac{1}{6} \cdot 2266776

Simplify

= 377796

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What is the integral from 2 to 3 of x^2(1+2x^3)^3 ?
The integral from 2 to 3 of x^2(1+2x^3)^3 is 377796