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

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- 4 x + \frac{2 x d y}{d x} = \frac{2 d y}{d x} + 3 x^{2} + 2

y = \frac{1}{( 1 + x ^{2} ) , at ( 1 , \frac{1}{2} )}

\int_{0}^{1} 1 + 7 x d x

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