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

The integral of (cos(x))/(sin(x)) is ln|sin(x)|+C

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

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

ln ∣ sin (x) ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = sin (x)

= ln ∣ sin (x) ∣

Add a constant to the solution

= ln ∣ sin (x) ∣ + C

\frac{d}{d x} (9 tan (\frac{x}{3}))

\frac{\partial}{\partial x} ((\frac{3 x ^{2}}{2 x + 4})^{3})

ln (\frac{e ^{t}}{1 + e ^{t}})

\frac{d}{d x} ((8 x^{2} - 7 y^{3})^{5})

\int \frac{4 x ^{2} + 4 x - 6}{( x - 6 ) ( x - 3 ) ^{2}} d x

What is the integral of (cos(x))/(sin(x)) ?
The integral of (cos(x))/(sin(x)) is ln|sin(x)|+C