What is the integral of cot^7(x) ?

The integral of cot^7(x) is -1/6 cot^6(x)+1/4 cot^4(x)-1/2 cot^2(x)-ln|sin(x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of cot^7(x)

\int cot^{7} (x) d x

- \frac{1}{6} cot^{6} (x) + \frac{1}{4} cot^{4} (x) - \frac{1}{2} cot^{2} (x) - ln ∣ sin (x) ∣ + C

Solution steps

\int cot^{7} (x) d x

Apply Integral Reduction

= - \frac{cot ^{6} ( x )}{6} - \int cot^{5} (x) d x

\int cot^{5} (x) d x = - \frac{1}{4} cot^{4} (x) + \frac{1}{2} cot^{2} (x) + ln ∣ sin (x) ∣

= - \frac{cot ^{6} ( x )}{6} - (- \frac{1}{4} cot^{4} (x) + \frac{1}{2} cot^{2} (x) + ln ∣ sin (x) ∣)

Simplify

- \frac{cot ^{6} ( x )}{6} - (- \frac{1}{4} cot^{4} (x) + \frac{1}{2} cot^{2} (x) + ln ∣ sin (x) ∣) : - \frac{1}{6} cot^{6} (x) + \frac{1}{4} cot^{4} (x) - \frac{1}{2} cot^{2} (x) - ln ∣ sin (x) ∣

= - \frac{1}{6} cot^{6} (x) + \frac{1}{4} cot^{4} (x) - \frac{1}{2} cot^{2} (x) - ln ∣ sin (x) ∣

Add a constant to the solution

= - \frac{1}{6} cot^{6} (x) + \frac{1}{4} cot^{4} (x) - \frac{1}{2} cot^{2} (x) - ln ∣ sin (x) ∣ + C

What is the integral of cot^7(x) ?
The integral of cot^7(x) is -1/6 cot^6(x)+1/4 cot^4(x)-1/2 cot^2(x)-ln|sin(x)|+C