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 x arctan (x + 1) d x

\int e^{- s t} cos (3 t) d t

\int x^{4} - 8 x d x

\int \frac{7 t ^{5}}{t ^{2} + 2} d t

\int (\frac{7}{6})^{x} d x

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