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

The integral of x^2sin(5/2)x^3sin(3/5)x^3 is 1/9 sin(5/2)sin(3/5)x^9+C

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

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

\frac{1}{9} sin (\frac{5}{2}) sin (\frac{3}{5}) x^{9} + C

Solution steps

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

Take the constant out:

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

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

Simplify

x^{2} x^{3} x^{3} : x^{8}

= sin (\frac{5}{2}) sin (\frac{3}{5}) \cdot \int x^{8} d x

Apply the Power Rule

= sin (\frac{5}{2}) sin (\frac{3}{5}) \frac{x ^{9}}{9}

Simplify

sin (\frac{5}{2}) sin (\frac{3}{5}) \frac{x ^{9}}{9} : \frac{1}{9} sin (\frac{5}{2}) sin (\frac{3}{5}) x^{9}

= \frac{1}{9} sin (\frac{5}{2}) sin (\frac{3}{5}) x^{9}

Add a constant to the solution

= \frac{1}{9} sin (\frac{5}{2}) sin (\frac{3}{5}) x^{9} + C

What is the integral of x^2sin(5/2)x^3sin(3/5)x^3 ?
The integral of x^2sin(5/2)x^3sin(3/5)x^3 is 1/9 sin(5/2)sin(3/5)x^9+C