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

The integral of 5cos(pix-3) is 5/pi sin(pix-3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 5cos(pix-3)

\int 5 cos (π x - 3) d x

\frac{5}{π} sin (π x - 3) + C

Solution steps

\int 5 cos (π x - 3) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int cos (π x - 3) d x

Rewrite using trig identities

= 5 \cdot \int cos (π x) cos (3) + sin (π x) sin (3) 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

= 5 (\int cos (π x) cos (3) d x + \int sin (π x) sin (3) d x)

\int cos (π x) cos (3) d x = cos (3) \frac{1}{π} sin (π x)

\int sin (π x) sin (3) d x = - \frac{1}{π} sin (3) cos (π x)

= 5 (cos (3) \frac{1}{π} sin (π x) - \frac{1}{π} sin (3) cos (π x))

Simplify

5 (cos (3) \frac{1}{π} sin (π x) - \frac{1}{π} sin (3) cos (π x)) : \frac{5}{π} sin (π x - 3)

= \frac{5}{π} sin (π x - 3)

Add a constant to the solution

= \frac{5}{π} sin (π x - 3) + C

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