What is the integral of-csc^2(5/2)x ?

The integral of-csc^2(5/2)x is -(csc^2(5/2)x^2)/2+C

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integral of-csc^2(5/2)x

\int - csc^{2} (\frac{5}{2}) x d x

- \frac{csc ^{2} ( \frac{5}{2} ) x ^{2}}{2} + C

Solution steps

\int - csc^{2} (\frac{5}{2}) x d x

Take the constant out:

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

= - csc^{2} (\frac{5}{2}) \cdot \int x d x

Apply the Power Rule

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

= - csc^{2} (\frac{5}{2}) \frac{x ^{2}}{2}

Multiply fractions:

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

= - \frac{csc ^{2} ( \frac{5}{2} ) x ^{2}}{2}

Add a constant to the solution

= - \frac{csc ^{2} ( \frac{5}{2} ) x ^{2}}{2} + C

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What is the integral of-csc^2(5/2)x ?
The integral of-csc^2(5/2)x is -(csc^2(5/2)x^2)/2+C