What is the integral of sin(pix)-cos(pix) ?

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

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integral of sin(pix)-cos(pix)

\int sin (π x) - cos (π x) d x

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

Solution steps

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

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

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

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

Add a constant to the solution

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

y^{\frac{1}{2}} (\frac{d y}{d x}) + y^{\frac{3}{2}} = 1

\frac{x ^{2} + 2 x - 5}{( x + 1 ) ^{2}}

f (x) = x - sin (x)

\frac{d}{d x} (\frac{4 x ^{2}}{e ^{2 x} sinh ( 2 x )})

\frac{d}{d x} ((- 4 + x^{2})^{- 1})

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