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

y \to 0 lim (\frac{2}{y ^{2} + y} - \frac{2}{y})

f (x) = 2^{l n (x)}

6 x^{2} - 9 x - 6, 7 x^{2} - 5 x - 3

x \to 0 lim (\frac{x}{5})

(x^{2} - 9)^{2} + 2

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