What is the integral of cos(2x)+sin(x) ?

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

\int cos (2 x) + sin (x) d x

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

Solution steps

\int cos (2 x) + 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 cos (2 x) d x + \int sin (x) d x

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

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

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

Add a constant to the solution

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

\int 10000 - x^{2} d x

y = x^{2} - 4 x, y = - 2 x

x \to 2 lim (- 2 x^{2})

4 x^{2}, \frac{1}{4} x

\frac{d}{d x} (tanh (ln (x)))

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