What is the integral of x^2*cos^3(7)x^3 ?

The integral of x^2*cos^3(7)x^3 is (cos^3(7)x^6)/6+C

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integral of x^2*cos^3(7)x^3

\int x^{2} \cdot cos^{3} (7) x^{3} d x

\frac{cos ^{3} ( 7 ) x ^{6}}{6} + C

Solution steps

\int x^{2} cos^{3} (7) x^{3} d x

Take the constant out:

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

= cos^{3} (7) \cdot \int x^{2} x^{3} d x

Simplify

x^{2} x^{3} : x^{5}

= cos^{3} (7) \cdot \int x^{5} d x

Apply the Power Rule

: \frac{x ^{6}}{6}

= cos^{3} (7) \frac{x ^{6}}{6}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{cos ^{3} ( 7 ) x ^{6}}{6}

Add a constant to the solution

= \frac{cos ^{3} ( 7 ) x ^{6}}{6} + C

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\frac{d}{d x} (3 x^{- 1} + 5 π)

\frac{\partial}{\partial x} (x^{3} e^{y} sin (x - y))

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What is the integral of x^2*cos^3(7)x^3 ?
The integral of x^2*cos^3(7)x^3 is (cos^3(7)x^6)/6+C