en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

- 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

Popular Examples

integral of (x^8)/(x^9-1)

\int \frac{x ^{8}}{x ^{9} - 1} d x

integral of (3x^5-8x^3+2)

\int (3 x^{5} - 8 x^{3} + 2) d x

integral of ((x^3-x^4)^2)/(sqrt(x))

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

integral of x/2 e^{-(3x)/4}

\int \frac{x}{2} e^{- \frac{3 x}{4}} d x

integral of 1/((3+cos(x)))

\int \frac{1}{( 3 + cos ( x ) )} d x

Frequently Asked Questions (FAQ)

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