Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

Summary Table Of Integrals

  • Page ID
    17442
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \begin{description}


    \item
    $\dst\int u^\alpha\; du={u^{\alpha+1}\over\alpha+1}+c$, \quad
    $\alpha\ne-1$

    \item
    $\dst\int{du\over u}=\ln|u|+c$


    \item
    $\dst\int\cos u\; du=\sin u+c$

    \item
    $\dst\int \sin u\; du=-\cos u+c$


    \item
    $\dst\int \tan u\; du=-\ln|\cos u|+c$
    \item
    $\dst\int \cot u\; du=\ln|\sin u|+c$

    \item
    $\dst\int \sec^2 u\; du=\tan u+c$

    \item
    $\dst\int \csc^2 u\; du=-\cot u+c$


    \item
    $\dst\int \sec u\; du=\ln|\sec u+\tan u|+c$


    \item
    $\dst\int\cos^2 u\; du={u\over2}+{1\over4}\sin2u
    +c$


    \item
    $\dst\int\sin^2 u\; du={u\over2}-{1\over4}\sin2u
    +c$

    \item
    $\dst\int {du\over 1+u^2}\; du=\tan^{-1}u+c$
    \item
    $\dst\int {du\over\sqrt{1-u^2}}\; du=\sin^{-1}u+c$
    \item
    $\dst\int {1\over u^2-1}\; du={1\over2}\ln\left|u-1\over u+1\right|+c$

    \item
    $\dst\int \cosh u\; du=\sinh u+c$


    \item
    $\dst\int \sinh u\; du=\cosh u+c$


    \item
    $\dst\int u\; dv=uv-\int v\; du$


    \item
    $\dst\int u\cos u\; du=u\sin u +\cos u+c$


    \item
    $\dst\int u\sin u\; du=-u\cos u +\sin u+c$


    \item
    $\dst\int ue^u\; du=ue^{u}-e^{u} +c$

    \item
    $\dst\int e^{\lambda u}\cos\omega u\; du={e^{\lambda u}(\lambda\cos
    \omega u+\omega\sin\omega u)\over \lambda^2+\omega^2}+c$

    \item
    $\dst\int e^{\lambda u}\sin\omega u\; du={e^{\lambda u}(\lambda\sin
    \omega u-\omega\cos\omega u)\over\lambda^2+\omega^2}+c$

    \item
    $\dst\int \ln|u|\; du=u\ln|u|-u+c$

    \item
    $\dst\int u\ln|u|\; du={u^2\ln|u|\over2}-{u^2\over4}+c$

    \item
    $\dst\int\cos\omega_1u\cos\omega_2u\,du={\sin
    (\omega_1+\omega_2)u\over2(\omega_1+\omega_2)}
    +{\sin(\omega_1-\omega_2)u\over2(\omega_1-\omega_2)}+c\quad
    (\omega_1\ne\pm
    \omega_2)$

    \item
    $\dst\int\sin\omega_1 u\sin\omega_2 u\,du=
    -{\sin(\omega_1+\omega_2)u\over2(\omega_1+\omega_2)}
    +{\sin(\omega_1-\omega_2)u\over2(\omega_1-\omega_2)}+c
    \quad
    (\omega_1\ne\pm
    \omega_2)$

    \item
    $\dst\int\sin\omega_1u\cos\omega_2 u\,du=-{\cos
    (\omega_1+\omega_2)u\over2(\omega_1+\omega_2)}
    -{\cos(\omega_1-\omega_2)u\over2(\omega_1-\omega_2)}+c\quad
    (\omega_1\ne\pm
    \omega_2)$