What is the integral of 1/(sin(x))(cos(x))/(sin(x)) ?

The integral of 1/(sin(x))(cos(x))/(sin(x)) is -csc(x)+C

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integral of 1/(sin(x))(cos(x))/(sin(x))

\int \frac{1}{sin ( x )} \frac{cos ( x )}{sin ( x )} d x

- csc (x) + C

Solution steps

\int \frac{1}{sin ( x )} \cdot \frac{cos ( x )}{sin ( x )} d x

Simplify

\frac{1}{sin ( x )} \cdot \frac{cos ( x )}{sin ( x )} : cot (x) csc (x)

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

Apply u-substitution

: \int - 1 d u

= \int - 1 d u

Integral of a constant:

\int a d x = a x

= (- 1) u

Substitute back

u = csc (x)

= (- 1) csc (x)

Simplify

= - csc (x)

Add a constant to the solution

= - csc (x) + C

h \to 0 lim (\frac{( 1 + h ) 3 - 1}{h})

x, y \to (0, 0) lim (\frac{( 2 x ^{2} y )}{x ^{2} + y ^{4}})

x \to 2 + lim (3 - x)

\frac{d}{d x} (\frac{2 ^{x}}{cos ( x )})

y^{^{''}} + 2 y^{^{'}} + y = 64 e^{(7 t)}

What is the integral of 1/(sin(x))(cos(x))/(sin(x)) ?
The integral of 1/(sin(x))(cos(x))/(sin(x)) is -csc(x)+C