
# Summary Table Of Integrals


$$\int u^\alpha\; du={u^{\alpha+1}\over\alpha+1}+c, \quad \alpha\ne-1$$
$$\int{du\over u}=\ln|u|+c$$
$$\int\cos u\; du=\sin u+c$$
$$\int \sin u\; du=-\cos u+c$$
$$\int \tan u\; du=-\ln|\cos u|+c$$
$$\int \cot u\; du=\ln|\sin u|+c$$
$$\int \sec^2 u\; du=\tan u+c$$
$$\int \csc^2 u\; du=-\cot u+c$$
$$\int \sec u\; du=\ln|\sec u+\tan u|+c$$
$$\int\cos^2 u\; du={u\over2}+{1\over4}\sin2u +c$$
$$\int\sin^2 u\; du={u\over2}-{1\over4}\sin2u +c$$
$$\int {du\over 1+u^2}\; du=\tan^{-1}u+c$$
$$\int {du\over\sqrt{1-u^2}}\; du=\sin^{-1}u+c$$
$$\int {1\over u^2-1}\; du={1\over2}\ln\left|u-1\over u+1\right|+c$$
$$\int \cosh u\; du=\sinh u+c$$
$$\int \sinh u\; du=\cosh u+c$$
$$\int u\; dv=uv-\int v\; du$$
$$\int u\cos u\; du=u\sin u +\cos u+c$$
$$\int u\sin u\; du=-u\cos u +\sin u+c$$
$$\int ue^u\; du=ue^{u}-e^{u} +c$$
$$\int e^{\lambda u}\cos\omega u\; du={e^{\lambda u}(\lambda\cos \omega u+\omega\sin\omega u)\over \lambda^2+\omega^2}+c$$
$$\int e^{\lambda u}\sin\omega u\; du={e^{\lambda u}(\lambda\sin \omega u-\omega\cos\omega u)\over\lambda^2+\omega^2}+c$$
$$\int \ln|u|\; du=u\ln|u|-u+c$$
$$\int u\ln|u|\; du={u^2\ln|u|\over2}-{u^2\over4}+c$$
$$\int\cos\omega_1u\cos\omega_2u\,du={\sin (\omega_1+\omega_2)u\over2(\omega_1+\omega_2)} +{\sin(\omega_1-\omega_2)u\over2(\omega_1-\omega_2)}+c\quad (\omega_1\ne\pm \omega_2)$$
$$\int\sin\omega_1 u\sin\omega_2 u\,du= -{\sin(\omega_1+\omega_2)u\over2(\omega_1+\omega_2)} +{\sin(\omega_1-\omega_2)u\over2(\omega_1-\omega_2)}+c \quad (\omega_1\ne\pm \omega_2)$$
$$\int\sin\omega_1u\cos\omega_2 u\,du=-{\cos (\omega_1+\omega_2)u\over2(\omega_1+\omega_2)} -{\cos(\omega_1-\omega_2)u\over2(\omega_1-\omega_2)}+c\quad (\omega_1\ne\pm \omega_2)$$