What is the integral of xcsc^2(a)x ?

The integral of xcsc^2(a)x is (x^3csc^2(a))/3+C

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integral of xcsc^2(a)x

\int x csc^{2} (a) x d x

\frac{x ^{3} csc ^{2} ( a )}{3} + C

Solution steps

\int x csc^{2} (a) x d x

Take the constant out:

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

= csc^{2} (a) \cdot \int xx d x

Simplify

xx : x^{2}

= csc^{2} (a) \cdot \int x^{2} d x

Apply the Power Rule

= csc^{2} (a) \frac{x ^{3}}{3}

Multiply fractions:

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

= \frac{x ^{3} csc ^{2} ( a )}{3}

Add a constant to the solution

= \frac{x ^{3} csc ^{2} ( a )}{3} + C

What is the integral of xcsc^2(a)x ?
The integral of xcsc^2(a)x is (x^3csc^2(a))/3+C