What is the integral of t/(sin^2(t)) ?

The integral of t/(sin^2(t)) is -tcot(t)+ln|sin(t)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of t/(sin^2(t))

\int \frac{t}{sin ^{2} ( t )} d t

- t cot (t) + ln ∣ sin (t) ∣ + C

Solution steps

\int \frac{t}{sin ^{2} ( t )} d t

Apply Integration By Parts

: - t cot (t) - \int - cot (t) d t

= - t cot (t) - \int - cot (t) d t

\int - cot (t) d t = - ln ∣ sin (t) ∣

= - t cot (t) - (- ln ∣ sin (t) ∣)

Simplify

= - t cot (t) + ln ∣ sin (t) ∣

Add a constant to the solution

= - t cot (t) + ln ∣ sin (t) ∣ + C

\int \frac{cosh ( ln ( x ) )}{x} d x

\int x^{3} (x^{4} + 5)^{3} d x

\int \frac{2 + 3 x}{x - 3} d x

\int x^{2} + 6 x + 9 d x

\int (2 x + 1) e^{- 2 x} d x

What is the integral of t/(sin^2(t)) ?
The integral of t/(sin^2(t)) is -tcot(t)+ln|sin(t)|+C