What is the integral of (θ-csc(θ)cot(θ)) ?

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

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integral of (θ-csc(θ)cot(θ))

\int (θ - csc (θ) cot (θ)) d θ

\frac{θ ^{2}}{2} + csc (θ) + C

Solution steps

\int θ - csc (θ) cot (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 θ d θ - \int csc (θ) cot (θ) d θ

\int θ d θ = \frac{θ ^{2}}{2}

\int csc (θ) cot (θ) d θ = - csc (θ)

= \frac{θ ^{2}}{2} - (- csc (θ))

Simplify

= \frac{θ ^{2}}{2} + csc (θ)

Add a constant to the solution

= \frac{θ ^{2}}{2} + csc (θ) + C

x \to \infty lim ((1)^{x})

\int \frac{4}{x ^{3} - 2 x ^{2}} d x

x y^{^{'}} - 2 y = 6 x^{2}

\int f (x, y, z) d x

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