What is the integral of cot^2(θ) ?

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

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integral of cot^2(θ)

\int cot^{2} (θ) d θ

- θ - cot (θ) + C

Solution steps

\int cot^{2} (θ) d θ

Rewrite using trig identities

= \int - 1 + csc^{2} (θ) d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 1 d θ + \int csc^{2} (θ) d θ

\int 1 d θ = θ

\int csc^{2} (θ) d θ = - cot (θ)

= - θ - cot (θ)

Add a constant to the solution

= - θ - cot (θ) + C

y^{^{'}} + \frac{y}{120} = 3

\int x^{4} (y - 2)

y = \frac{4 x ^{2} + 6 x + 8}{x}

x^{2} \frac{d y}{d x} - 2 x y = 5 y^{4}, y (1) = \frac{1}{3}

\int (\frac{sec ( x ) + cos ( x )}{2 cos ( x )}) d x