What is the integral of 12sec(2x)tan(2x) ?

The integral of 12sec(2x)tan(2x) is 12(1/2 cos(2x)+1/2 sin(2x)tan(2x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 12sec(2x)tan(2x)

\int 12 sec (2 x) tan (2 x) d x

12 (\frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x)) + C

Solution steps

\int 12 sec (2 x) tan (2 x) d x

Take the constant out:

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

= 12 \cdot \int sec (2 x) tan (2 x) d x

Rewrite using trig identities

= 12 \cdot \int \frac{sin ( 2 x )}{cos ^{2} ( 2 x )} d x

Apply Integration By Parts

: - \int sin (2 x) d x + \frac{1}{2} sin (2 x) tan (2 x)

= 12 (- \int sin (2 x) d x + \frac{1}{2} sin (2 x) tan (2 x))

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

= 12 (- (- \frac{1}{2} cos (2 x)) + \frac{1}{2} sin (2 x) tan (2 x))

Simplify

= 12 (\frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x))

Add a constant to the solution

= 12 (\frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x)) + C

\int ln^{2} (x^{20}) d x

\int csc (1 - 5 x) d x

\int \frac{cos ( 3 x )}{x} d x

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

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

What is the integral of 12sec(2x)tan(2x) ?
The integral of 12sec(2x)tan(2x) is 12(1/2 cos(2x)+1/2 sin(2x)tan(2x))+C