What is the integral of (3cos(3x)-5sin(5x)) ?

The integral of (3cos(3x)-5sin(5x)) is sin(3x)+cos(5x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3cos(3x)-5sin(5x))

\int (3 cos (3 x) - 5 sin (5 x)) d x

sin (3 x) + cos (5 x) + C

Solution steps

\int 3 cos (3 x) - 5 sin (5 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 3 cos (3 x) d x - \int 5 sin (5 x) d x

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

\int 5 sin (5 x) d x = - cos (5 x)

= sin (3 x) - (- cos (5 x))

Simplify

= sin (3 x) + cos (5 x)

Add a constant to the solution

= sin (3 x) + cos (5 x) + C

f (x) = 3 - x

\int_{9}^{1} (- 15 x) d x

t \to 0 lim (\frac{t ^{3} - 1}{t - 1})

\frac{d}{d x} (\frac{6}{( x - 3 ) ^{4}})

\int 7 x \cdot \frac{e ^{3 x}}{7} d x

What is the integral of (3cos(3x)-5sin(5x)) ?
The integral of (3cos(3x)-5sin(5x)) is sin(3x)+cos(5x)+C