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$$\begin{array}{cc} f&\int f\\ \hline x^\alpha&\frac{x^{\alpha+1}}{\alpha+1}\\ \frac{1}{x}&\ln\\ \exp&\exp\\ \sin&-\cos\\ \cos&\sin\\ \sinh&\cosh\\ \cosh&\sinh\\ \ln x&x\ln x-x\\ udv&uv-\int vdu\\ \end{array}$$
Paul's Derivatives/Integrals