Finding antiderivatives

Summary

• Antiderivative of a constant. For any constant $k$ ,

$$\int{ ‍ }kdx=kx+C$$

• Antiderivative of $x$ .

$$\int{ ‍ }xdx=x^2/2+c$$

• Antiderivative of power function. If $a≠-1$ then

$$\int{ ‍ }x^adx= \frac{x^{a+1}}{a+1}+C$$

• Antiderivative of $x^{-1}= \frac{1}{x}$

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

• Constant law. For any constant $c$ ,

$$\int{ ‍ }cf\left( x \right)dx=c\int{ ‍ }f\left( x \right)dx$$

• Addition law.

$$\int{ ‍ }\left( f\left( x \right)+g\left( x \right) \right)dx=\int{ ‍ }f\left( x \right)dx+\int{ ‍ }g\left( x \right)dx$$