Can you help me with this, please?

$$\int\sqrt{a\sin(bx)+c} \, dx$$

I thank you in advance for your help.

  • 2
    $\begingroup$ This is one of the elliptic integrals: WA. $\endgroup$ – J. W. Perry Aug 5 '14 at 6:07
  • $\begingroup$ I've tried some substitutions, but I haven't been able to solve it till now. $\endgroup$ – distressed Aug 5 '14 at 6:12
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    $\begingroup$ Incomplete elliptic integral of the second kind @J.W.Perry $\endgroup$ – ClassicStyle Aug 5 '14 at 6:14
  • $\begingroup$ An elliptic integral of the second kind? - That sounds very special! Don't know anything about it.^^ $\endgroup$ – distressed Aug 5 '14 at 6:16
  • $\begingroup$ @distressed It is actually quite interesting. Start be reading the wiki on Elliptic Integrals. $\endgroup$ – J. W. Perry Aug 5 '14 at 6:17

If $a=c$, or $b=0$, then the integral can be expressed in terms of elementary trigonometric functions, otherwise elliptic integrals must be employed.

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