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

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

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integral of sin(pi)x-3sin(3x)

\int sin (π) x - 3 sin (3 x) d x

cos (3 x) + C

Solution steps

\int sin (π) 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 sin (π) x d x - \int 3 sin (3 x) d x

\int sin (π) x d x = 0

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

= 0 - (- cos (3 x))

Simplify

= cos (3 x)

Add a constant to the solution

= cos (3 x) + C

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