What is the integral of (csc(x))/(csc(x)-sin(x)) ?

The integral of (csc(x))/(csc(x)-sin(x)) is tan(x)+C

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integral of (csc(x))/(csc(x)-sin(x))

\int \frac{csc ( x )}{csc ( x ) - sin ( x )} d x

tan (x) + C

Solution steps

\int \frac{csc ( x )}{csc ( x ) - sin ( x )} d x

Simplify

\frac{csc ( x )}{csc ( x ) - sin ( x )} : sec^{2} (x)

= \int sec^{2} (x) d x

Use the common integral:

\int sec^{2} (x) d x = tan (x)

= tan (x)

Add a constant to the solution

= tan (x) + C

\frac{d y}{d t} + y = t e^{t}

f (x) = \frac{1}{2 x}, at x = 36

f (x) = \frac{tan ( 9 x )}{1 + sin ( 9 x )}

(2 x + 3 y - 1) d x - 4 (x + 1) d y = 0

What is the integral of (csc(x))/(csc(x)-sin(x)) ?
The integral of (csc(x))/(csc(x)-sin(x)) is tan(x)+C