What is the integral of cos(x)(sec(x)+tan(x)) ?

The integral of cos(x)(sec(x)+tan(x)) is x-cos(x)+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)(sec(x)+tan(x))

\int cos (x) (sec (x) + tan (x)) d x

x - cos (x) + C

Solution steps

\int cos (x) (sec (x) + tan (x)) d x

Rewrite using trig identities

= \int 1 + sin (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

= \int 1 d x + \int sin (x) d x

\int 1 d x = x

\int sin (x) d x = - cos (x)

= x - cos (x)

Add a constant to the solution

= x - cos (x) + C

\int (x - 5) (3 x + 4) d x

\int (5 x^{3} + 6 x^{3} - 5) d x

\int (5 x + 2)^{7} d x

\int (2 t^{2} - 3)^{2} d t

What is the integral of cos(x)(sec(x)+tan(x)) ?
The integral of cos(x)(sec(x)+tan(x)) is x-cos(x)+C