What is the integral of cos(x)sin(x)tan(x) ?

The integral of cos(x)sin(x)tan(x) is 1/2 (x-1/2 sin(2x))+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)sin(x)tan(x)

\int cos (x) sin (x) tan (x) d x

\frac{1}{2} (x - \frac{1}{2} sin (2 x)) + C

Solution steps

\int cos (x) sin (x) tan (x) d x

Rewrite using trig identities

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

Take the constant out:

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

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 1 d x = x

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

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

Add a constant to the solution

= \frac{1}{2} (x - \frac{1}{2} sin (2 x)) + C

\int \frac{( 2 x ^{2} - x + 4 )}{( x ^{3} + 4 x )} d x

\int \frac{ln ( 8 x )}{x ^{3}} d x

\int (x \cdot e^{x^{2}}) d x

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

\int (12 x^{2} - 7 x + 2) d x

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