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

The integral of (xcos(3)x^2)/(sin^3(3)x^2) is (cos(3)}{sin^3(3)}*\frac{x^2)/2+C

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

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

\frac{cos ( 3 )}{sin ^{3} ( 3 )} \cdot \frac{x ^{2}}{2} + C

Solution steps

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

Take the constant out:

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

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

Simplify

\frac{x x ^{2}}{x ^{2}} : x

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

Apply the Power Rule

: \frac{x ^{2}}{2}

= \frac{cos ( 3 )}{sin ^{3} ( 3 )} \cdot \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{cos ( 3 )}{sin ^{3} ( 3 )} \cdot \frac{x ^{2}}{2} + C

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What is the integral of (xcos(3)x^2)/(sin^3(3)x^2) ?
The integral of (xcos(3)x^2)/(sin^3(3)x^2) is (cos(3)}{sin^3(3)}*\frac{x^2)/2+C