Indefinite Integration

$\frac{x}{2}-\frac{\sin \pi x}{2 \pi}+\mathrm{c}$, (where c is a constant of integration)

$\frac{1}{2} x-\frac{\sin 2 \pi x}{4 \pi}+\mathrm{c}$, (where c is a constant of integration)

$\frac{x}{2}-\frac{\cos \pi x}{2 \pi}+\mathrm{c}$, (where c is a constant of integration)

$\frac{1}{1+\pi^x}+\frac{\cos ^2 \pi x}{2 \pi}+\mathrm{c}$, (where c is a constant of integration)