What is the integral of cot^3(2t) ?

The integral of cot^3(2t) is 1/2 (-(cot^2(2t))/2-ln|sin(2t)|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of cot^3(2t)

\int cot^{3} (2 t) d t

\frac{1}{2} (- \frac{cot ^{2} ( 2 t )}{2} - ln ∣ sin (2 t) ∣) + C

Solution steps

\int cot^{3} (2 t) d t

Apply u-substitution

= \int cot^{3} (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int cot^{3} (u) d u

Apply Integral Reduction

= \frac{1}{2} (- \frac{cot ^{2} ( u )}{2} - \int cot (u) d u)

\int cot (u) d u = ln ∣ sin (u) ∣

= \frac{1}{2} (- \frac{cot ^{2} ( u )}{2} - ln ∣ sin (u) ∣)

Substitute back

u = 2 t

= \frac{1}{2} (- \frac{cot ^{2} ( 2 t )}{2} - ln ∣ sin (2 t) ∣)

Add a constant to the solution

= \frac{1}{2} (- \frac{cot ^{2} ( 2 t )}{2} - ln ∣ sin (2 t) ∣) + C

\int - 0.5 e^{- 0.01 x} d x

\int \frac{1}{( 1 - x ^{3} )} d x

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

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

\int e^{7 x} x d x

What is the integral of cot^3(2t) ?
The integral of cot^3(2t) is 1/2 (-(cot^2(2t))/2-ln|sin(2t)|)+C