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.
\[\int{ }\left( f\left( x \right)+g\left( x \right) \right)dx=\int{ }f\left( x \right)dx+\int{ }g\left( x \right)dx\]