What is the integral of x^2cos(4)x^3 ?

The integral of x^2cos(4)x^3 is 1/6 cos(4)x^6+C

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integral of x^2cos(4)x^3

\int x^{2} cos (4) x^{3} d x

\frac{1}{6} cos (4) x^{6} + C

Solution steps

\int x^{2} cos (4) x^{3} d x

Take the constant out:

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

= cos (4) \cdot \int x^{2} x^{3} d x

Simplify

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

= cos (4) \cdot \int x^{5} d x

Apply the Power Rule

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

= cos (4) \frac{x ^{6}}{6}

Simplify

cos (4) \frac{x ^{6}}{6} : \frac{1}{6} cos (4) x^{6}

= \frac{1}{6} cos (4) x^{6}

Add a constant to the solution

= \frac{1}{6} cos (4) x^{6} + C

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What is the integral of x^2cos(4)x^3 ?
The integral of x^2cos(4)x^3 is 1/6 cos(4)x^6+C