What is the integral from 0 to 2 of x^3(2+x^4)^3 ?

The integral from 0 to 2 of x^3(2+x^4)^3 is 6560

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integral from 0 to 2 of x^3(2+x^4)^3

\int_{0}^{2} x^{3} (2 + x^{4})^{3} d x

6560

Solution steps

\int_{0}^{2} x^{3} (2 + x^{4})^{3} d x

Apply u-substitution

: \int_{2}^{18} \frac{u ^{3}}{4} d u

= \int_{2}^{18} \frac{u ^{3}}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int_{2}^{18} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{2}^{18}

= \frac{1}{4} [\frac{u ^{4}}{4}]_{2}^{18}

Compute the boundaries:

26240

= \frac{1}{4} \cdot 26240

Simplify

= 6560

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

\int_{0}^{4} (\frac{1}{2 x + 1}) d x

What is the integral from 0 to 2 of x^3(2+x^4)^3 ?
The integral from 0 to 2 of x^3(2+x^4)^3 is 6560