主な関数の積分

• $$\int x^p dx = \frac{1}{p+1}x^{p+1}+C, \quad(p\ne-1)$$
• $$\int \frac{1}{\sqrt{x}} dx = 2\sqrt{x}+C$$
• $$\int \frac{1}{x}dx = \ln \vert x\vert + C$$
• $$\int \cos\omega t dt = \frac{1}{\omega}\sin\omega t + C$$
• $$\int \sin\omega t dt = -\frac{1}{\omega}\cos t + C$$
• $$\int e^{at} dt = \frac{1}{a}e^{at} + C$$
• $$\int \frac{1}{x}dx=\log x+C$$

$C$: 積分定数