en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (csc(θ)cot(θ))/(1-csc(θ))

Solution

\int \frac{csc ( θ ) cot ( θ )}{1 - csc ( θ )} d θ

Solution

ln ∣ 1 - csc (θ) ∣ + C

Solution steps

\int \frac{csc ( θ ) cot ( θ )}{1 - csc ( θ )} d θ

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 = 1 - csc (θ)

= ln ∣ 1 - csc (θ) ∣

Add a constant to the solution

= ln ∣ 1 - csc (θ) ∣ + C

Popular Examples

integral of tan^3(4x)sec^{9/2}(4x)

\int tan^{3} (4 x) sec^{\frac{9}{2}} (4 x) d x

integral of 1/(sqrt(x^2+r^2))

\int \frac{1}{x ^{2} + r ^{2}} d x

integral of (8x^3+6x-5)/(2x^4+3x^2-5x)

\int \frac{8 x ^{3} + 6 x - 5}{2 x ^{4} + 3 x ^{2} - 5 x} d x

integral of (x^2+3x-4)/(x+1)

\int \frac{x ^{2} + 3 x - 4}{x + 1} d x

integral of 1/(sqrt(x-16))

\int \frac{1}{x - 16} d x

Frequently Asked Questions (FAQ)

What is the integral of (csc(θ)cot(θ))/(1-csc(θ)) ?
The integral of (csc(θ)cot(θ))/(1-csc(θ)) is ln|1-csc(θ)|+C