What is the integral of cot^2(θ)csc^2(θ) ?

The integral of cot^2(θ)csc^2(θ) is -(cot^3(θ))/3+C

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integral of cot^2(θ)csc^2(θ)

\int cot^{2} (θ) csc^{2} (θ) d θ

- \frac{cot ^{3} ( θ )}{3} + C

Solution steps

\int cot^{2} (θ) csc^{2} (θ) d θ

Apply u-substitution

: \int - u^{2} d u

= \int - u^{2} d u

Take the constant out:

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

= - \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= - \frac{u ^{3}}{3}

Substitute back

u = cot (θ)

= - \frac{cot ^{3} ( θ )}{3}

Add a constant to the solution

= - \frac{cot ^{3} ( θ )}{3} + C

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\int \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} d x

What is the integral of cot^2(θ)csc^2(θ) ?
The integral of cot^2(θ)csc^2(θ) is -(cot^3(θ))/3+C