What is the integral of x^2((x^3)/(12)+4)^3 ?

The integral of x^2((x^3)/(12)+4)^3 is ((x^3)/(12)+4)^4+C

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integral of x^2((x^3)/(12)+4)^3

\int x^{2} (\frac{x ^{3}}{12} + 4)^{3} d x

(\frac{x ^{3}}{12} + 4)^{4} + C

Solution steps

\int x^{2} (\frac{x ^{3}}{12} + 4)^{3} d x

Apply u-substitution

= \int 4 u^{3} d u

Take the constant out:

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

= 4 \cdot \int u^{3} d u

Apply the Power Rule

= 4 \cdot \frac{u ^{4}}{4}

Substitute back

u = \frac{x ^{3}}{12} + 4

= 4 \cdot \frac{( \frac{x ^{3}}{12} + 4 ) ^{4}}{4}

Simplify

4 \cdot \frac{( \frac{x ^{3}}{12} + 4 ) ^{4}}{4} : (\frac{x ^{3}}{12} + 4)^{4}

= (\frac{x ^{3}}{12} + 4)^{4}

Add a constant to the solution

= (\frac{x ^{3}}{12} + 4)^{4} + C

What is the integral of x^2((x^3)/(12)+4)^3 ?
The integral of x^2((x^3)/(12)+4)^3 is ((x^3)/(12)+4)^4+C