What is the integral of (1-csc(t)cot(t)) ?

The integral of (1-csc(t)cot(t)) is t+csc(t)+C

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integral of (1-csc(t)cot(t))

\int (1 - csc (t) cot (t)) d t

t + csc (t) + C

Solution steps

\int 1 - csc (t) cot (t) d t

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

\int 1 d t = t

\int csc (t) cot (t) d t = - csc (t)

= t - (- csc (t))

Simplify

= t + csc (t)

Add a constant to the solution

= t + csc (t) + C

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\frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{2}} + 3 x)

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What is the integral of (1-csc(t)cot(t)) ?
The integral of (1-csc(t)cot(t)) is t+csc(t)+C