What is the integral of x^2sin(5)x^3 ?

The integral of x^2sin(5)x^3 is 1/6 sin(5)x^6+C

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integral of x^2sin(5)x^3

\int x^{2} sin (5) x^{3} d x

\frac{1}{6} sin (5) x^{6} + C

Solution steps

\int x^{2} sin (5) x^{3} d x

Take the constant out:

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

= sin (5) \cdot \int x^{2} x^{3} d x

Simplify

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

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

Apply the Power Rule

= sin (5) \frac{x ^{6}}{6}

Simplify

sin (5) \frac{x ^{6}}{6} : \frac{1}{6} sin (5) x^{6}

= \frac{1}{6} sin (5) x^{6}

Add a constant to the solution

= \frac{1}{6} sin (5) x^{6} + C

in t e g r a l y^{- 2}

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What is the integral of x^2sin(5)x^3 ?
The integral of x^2sin(5)x^3 is 1/6 sin(5)x^6+C