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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2sin(x)-cos(x))

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

- 2 cos (x) - sin (x) + C

Solution steps

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

\int 2 sin (x) d x = - 2 cos (x)

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

= - 2 cos (x) - sin (x)

Add a constant to the solution

= - 2 cos (x) - sin (x) + C

\int \frac{2 x ^{4} + 6 x ^{3} - x}{x ^{3}} d x

\frac{d}{d x} (2 x + \frac{2}{x})

y = e^{x}, y = e^{2 x - 1}, x = 0

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

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

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