What is the integral of 64x^3(u)^3 ?

The integral of 64x^3(u)^3 is 16x^3u^4+C

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integral of 64x^3(u)^3

\int 64 x^{3} (u)^{3} d u

16 x^{3} u^{4} + C

Solution steps

\int 64 x^{3} u^{3} d u

Take the constant out:

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

= 64 x^{3} \cdot \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= 64 x^{3} \frac{u ^{4}}{4}

Simplify

64 x^{3} \frac{u ^{4}}{4} : 16 x^{3} u^{4}

= 16 x^{3} u^{4}

Add a constant to the solution

= 16 x^{3} u^{4} + C

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