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

The integral of sin(pix)-3sin(3x) is -1/pi cos(pix)+cos(3x)+C

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

\int sin (π x) - 3 sin (3 x) d x

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

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

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

Simplify

= - \frac{1}{π} cos (π x) + cos (3 x)

Add a constant to the solution

= - \frac{1}{π} cos (π x) + cos (3 x) + C

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What is the integral of sin(pix)-3sin(3x) ?
The integral of sin(pix)-3sin(3x) is -1/pi cos(pix)+cos(3x)+C