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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \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

\int cos (πn t) d t

n = 1 \sum \infty (\frac{π}{6})^{n}

(tan (x))^{\frac{3}{x}}

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = 7 + e^{\frac{x}{2}}

\int t (t^{6} + t - 5) d t

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