What is the integral of cos^4(y) ?

The integral of cos^4(y) is cos^3(y)sin(y)+3/8 (y-1/4 sin(4y))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of cos^4(y)

\int cos^{4} (y) d y

cos^{3} (y) sin (y) + \frac{3}{8} (y - \frac{1}{4} sin (4 y)) + C

Solution steps

\int cos^{4} (y) d y

Simplify

cos^{4} (y) : cos^{3} (y) cos (y)

= \int cos^{3} (y) cos (y) d y

Apply Integration By Parts

= cos^{3} (y) sin (y) - \int - 3 cos^{2} (y) sin^{2} (y) d y

\int - 3 cos^{2} (y) sin^{2} (y) d y = - \frac{3}{8} (y - \frac{1}{4} sin (4 y))

= cos^{3} (y) sin (y) - (- \frac{3}{8} (y - \frac{1}{4} sin (4 y)))

Simplify

= cos^{3} (y) sin (y) + \frac{3}{8} (y - \frac{1}{4} sin (4 y))

Add a constant to the solution

= cos^{3} (y) sin (y) + \frac{3}{8} (y - \frac{1}{4} sin (4 y)) + C

What is the integral of cos^4(y) ?
The integral of cos^4(y) is cos^3(y)sin(y)+3/8 (y-1/4 sin(4y))+C