What is the integral of (cos(5x)-sec^2(x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (cos(5x)-sec^2(x))

\int (cos (5 x) - sec^{2} (x)) d x

\frac{1}{5} sin (5 x) - tan (x) + C

Solution steps

\int cos (5 x) - sec^{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

= \int cos (5 x) d x - \int sec^{2} (x) d x

\int cos (5 x) d x = \frac{1}{5} sin (5 x)

\int sec^{2} (x) d x = tan (x)

= \frac{1}{5} sin (5 x) - tan (x)

Add a constant to the solution

= \frac{1}{5} sin (5 x) - tan (x) + C

\int \frac{x - 3}{x ^{4} + 9 x ^{2}} d x

\int x - 3 x d x

\int 16 sec^{2} (x) tan^{7} (x) d x

\int \frac{e ^{x}}{1 + x} d x

\int \frac{1}{100 + x ^{2}} d x

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