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

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

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

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

x + csc (x) + C

Solution steps

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

\int 1 d x = x

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

= x - (- csc (x))

Simplify

= x + csc (x)

Add a constant to the solution

= x + csc (x) + C

\int x 4 + 9 x^{2} d x

f (x) = \frac{x}{x ^{2} + 25}

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

f (x) = x^{2} - 3 x + 1, at x = 3

n = 2 \sum \infty \frac{1}{( 3 n - 2 ) ^{5}}

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