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

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

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

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

- cot (x) + csc (x) + C

Solution steps

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

Expand

csc (x) (csc (x) - cot (x)) : csc^{2} (x) - csc (x) cot (x)

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

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

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

= - cot (x) - (- csc (x))

Simplify

= - cot (x) + csc (x)

Add a constant to the solution

= - cot (x) + csc (x) + C

\frac{1}{s ^{2} + 5 s}

y = x^{3} - 2 x^{2} + 5, (2, 5)

x^{2} y^{^{'}} + 2 x y = ln (x), y (1) = 8

\int \frac{x}{( x + 1 ) ^{2}} d x

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

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