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12.1: A- Short Table of Integrals

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    108000
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    Appendix A A Short Table of Integrals
    a. \[\int \frac{d u}{a^2+u^2}=\frac{1}{a} \arctan \left(\frac{u}{a}\right)+C\]

    b. \[\int \frac{d u}{\sqrt{u^2 \pm a^2}}=\ln \left|u+\sqrt{u^2 \pm a^2}\right|+C\]

    c. \[\int \sqrt{u^2 \pm a^2} d u=\frac{u}{2} \sqrt{u^2 \pm a^2} \pm \frac{a^2}{2} \ln \left|u+\sqrt{u^2 \pm a^2}\right|+C\]

    d. \[\int \frac{u^2 d u}{\sqrt{u^2 \pm a^2}}=\frac{u}{2} \sqrt{u^2 \pm a^2} \mp \frac{a^2}{2} \ln \left|u+\sqrt{u^2 \pm a^2}\right|+C\]

    e. \[\int \frac{d u}{u \sqrt{u^2+a^2}}=-\frac{1}{a} \ln \left|\frac{a+\sqrt{u^2+a^2}}{u}\right|+C\]

    f. \[\int \frac{d u}{u \sqrt{u^2-a^2}}=\frac{1}{a} \operatorname{arcsec}\left(\frac{u}{a}\right)+C\]

    g. \[\int \frac{d u}{\sqrt{a^2-u^2}}=\arcsin \left(\frac{u}{a}\right)+C\]

    h. \[\int \sqrt{a^2-u^2} d u=\frac{u}{2} \sqrt{a^2-u^2}+\frac{a^2}{2} \arcsin \left(\frac{u}{a}\right)+C\]

    i. \[\int \frac{u^2}{\sqrt{a^2-u^2}} d u=-\frac{u}{2} \sqrt{a^2-u^2}+\frac{a^2}{2} \arcsin \left(\frac{u}{a}\right)+C\]

    j. \[\int \frac{d u}{u \sqrt{a^2-u^2}}=-\frac{1}{a} \ln \left|\frac{a+\sqrt{a^2-u^2}}{u}\right|+C\]

    k. \[\int \frac{d u}{u^2 \sqrt{a^2-u^2}}=-\frac{\sqrt{a^2-u^2}}{a^2 u}+C\]


    This page titled 12.1: A- Short Table of Integrals is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Matthew Boelkins, David Austin & Steven Schlicker (ScholarWorks @Grand Valley State University) .

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