What is the integral of cos(x)cos^2(3x) ?

The integral of cos(x)cos^2(3x) is cos^2(3x)sin(x)+3/2 (-1/7 sin(7x)+1/5 sin(5x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(x)cos^2(3x)

\int cos (x) cos^{2} (3 x) d x

cos^{2} (3 x) sin (x) + \frac{3}{2} (- \frac{1}{7} sin (7 x) + \frac{1}{5} sin (5 x)) + C

Solution steps

\int cos (x) cos^{2} (3 x) d x

Apply Integration By Parts

: cos^{2} (3 x) sin (x) - \int - 3 sin (6 x) sin (x) d x

= cos^{2} (3 x) sin (x) - \int - 3 sin (6 x) sin (x) d x

\int - 3 sin (6 x) sin (x) d x = - \frac{3}{2} (- \frac{1}{7} sin (7 x) + \frac{1}{5} sin (5 x))

= cos^{2} (3 x) sin (x) - (- \frac{3}{2} (- \frac{1}{7} sin (7 x) + \frac{1}{5} sin (5 x)))

Simplify

= cos^{2} (3 x) sin (x) + \frac{3}{2} (- \frac{1}{7} sin (7 x) + \frac{1}{5} sin (5 x))

Add a constant to the solution

= cos^{2} (3 x) sin (x) + \frac{3}{2} (- \frac{1}{7} sin (7 x) + \frac{1}{5} sin (5 x)) + C

\int e^{l n (3 c o s (x))} d x

\int \frac{ln ( x ^{4} )}{x ^{3}} d x

\int \frac{3}{1 + 9 y ^{2}} d y

\int 500 - \frac{x}{3} d x

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

What is the integral of cos(x)cos^2(3x) ?
The integral of cos(x)cos^2(3x) is cos^2(3x)sin(x)+3/2 (-1/7 sin(7x)+1/5 sin(5x))+C