What is the integral of (csc^2(x)-1) ?

The integral of (csc^2(x)-1) is -cot(x)-x+C

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integral of (csc^2(x)-1)

\int (csc^{2} (x) - 1) d x

- cot (x) - x + C

Solution steps

\int csc^{2} (x) - 1 d x

Apply the Sum Rule:

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

= \int csc^{2} (x) d x - \int 1 d x

\int csc^{2} (x) d x = - cot (x)

\int 1 d x = x

= - cot (x) - x

Add a constant to the solution

= - cot (x) - x + C

\int (x^{'}) d x

\int x + e^{- 2 x} d x

\int \frac{12}{x ^{5}} + \frac{1}{4 x ^{8}} + \frac{6}{7 x ^{2}} d x

\int \frac{1}{( x + 1 ) ^{9}} d x

\int \frac{3 x ^{2}}{( x ^{3} + 5 ) ^{2}} d x

What is the integral of (csc^2(x)-1) ?
The integral of (csc^2(x)-1) is -cot(x)-x+C