What is the integral of (cos(8x))/(cos^2(4x)) ?

The integral of (cos(8x))/(cos^2(4x)) is 1/4 cos(8x)tan(4x)+1/4 (8x-sin(8x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(8x))/(cos^2(4x))

\int \frac{cos ( 8 x )}{cos ^{2} ( 4 x )} d x

\frac{1}{4} cos (8 x) tan (4 x) + \frac{1}{4} (8 x - sin (8 x)) + C

Solution steps

\int \frac{cos ( 8 x )}{cos ^{2} ( 4 x )} d x

Apply Integration By Parts

: \frac{1}{4} cos (8 x) tan (4 x) - \int - 2 sin (8 x) tan (4 x) d x

= \frac{1}{4} cos (8 x) tan (4 x) - \int - 2 sin (8 x) tan (4 x) d x

\int - 2 sin (8 x) tan (4 x) d x = - \frac{1}{4} (8 x - sin (8 x))

= \frac{1}{4} cos (8 x) tan (4 x) - (- \frac{1}{4} (8 x - sin (8 x)))

Simplify

= \frac{1}{4} cos (8 x) tan (4 x) + \frac{1}{4} (8 x - sin (8 x))

Add a constant to the solution

= \frac{1}{4} cos (8 x) tan (4 x) + \frac{1}{4} (8 x - sin (8 x)) + C

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

\int \frac{1}{9 - x} d x

\int sin (\frac{3 x}{2}) d x

\int sin^{7} (x) cos^{3} (x) d x

x \to 0 lim (x^{19 x})

What is the integral of (cos(8x))/(cos^2(4x)) ?
The integral of (cos(8x))/(cos^2(4x)) is 1/4 cos(8x)tan(4x)+1/4 (8x-sin(8x))+C