$$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ (where $n \neq -1$)

Example: $\int x^2 \, dx = \frac{x^3}{3} + C$

$$\int e^x \, dx = e^x + C$$

$$\int a^x \, dx = \frac{a^x}{\ln(a)} + C$$

$$\int \sin(x) \, dx = -\cos(x) + C$$

$$\int \cos(x) \, dx = \sin(x) + C$$

$$\int \frac{1}{x} \, dx = \ln|x| + C$$

$$\int \ln(x) \, dx = x\ln(x) - x + C$$

$$\int \frac{1}{\sqrt{1-x^2}} \, dx = \arcsin(x) + C$$

$$\int \frac{1}{1+x^2} \, dx = \arctan(x) + C$$

$$\int u \, dv = uv - \int v \, du$$

Example: $\int x e^x \, dx = xe^x - e^x + C$