Answer
$-\cos\hspace{0.5mm}\pi x+C$
Work Step by Step
$\int\pi\sin\hspace{0.5mm}\pi x\hspace{0.5mm}dx$
Let $u=\pi x\hspace{8mm}du=\pi dx\hspace{8mm}dx=\frac{du}{\pi}$
$\int\pi\sin\hspace{0.5mm}\pi x\hspace{0.5mm}dx=\int\pi\sin\hspace{0.5mm}u\hspace{0.5mm}\frac{du}{\pi}=\int\sin{u}du=-\cos{u}+C$
$=-\cos\hspace{0.5mm}\pi x+C$
