What is the integral of (2cos(2x)-3sin(3x)) ?

The integral of (2cos(2x)-3sin(3x)) is sin(2x)+cos(3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2cos(2x)-3sin(3x))

\int (2 cos (2 x) - 3 sin (3 x)) d x

sin (2 x) + cos (3 x) + C

Solution steps

\int 2 cos (2 x) - 3 sin (3 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 cos (2 x) d x - \int 3 sin (3 x) d x

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

\int 3 sin (3 x) d x = - cos (3 x)

= sin (2 x) - (- cos (3 x))

Simplify

= sin (2 x) + cos (3 x)

Add a constant to the solution

= sin (2 x) + cos (3 x) + C

\int x^{2} \cdot 3 x d x

- e^{- x}

\int \frac{x + 1}{x ^{2} - 2 x + 3} d x

\int r e^{k r} d r

\int 6 cos (x) sin (x) d x

What is the integral of (2cos(2x)-3sin(3x)) ?
The integral of (2cos(2x)-3sin(3x)) is sin(2x)+cos(3x)+C