I'm trying to find this indefinite integral

$$\int\frac{\cos^{3/2} x}{\sin x\sqrt{(\lambda-2\cos x-2\ln(1-\cos x)+2\ln(\sin x))}} \,\mathrm dx$$

Or $$\int_0^{\pi/2}\frac{\cos^{3/2}x}{\sin x\sqrt{\lambda-2\cos x-2\ln(1-\cos x)+2\ln(\sin x)}}\,\mathrm dx$$

Where $\lambda>2$

Which sub I take !?

I don't have any ideas for this type integration

Please give me ideas enter image description here

  • $\begingroup$ You should edit your question so we can properly see the integral.. I'm not exactly sure what you typed in or I'd edit it myself $\endgroup$ – joseph May 2 at 14:34
  • $\begingroup$ Yes sir correct , thank you very much $\endgroup$ – user670134 May 2 at 14:40
  • $\begingroup$ Where did you find this integral? do you know if it has a closed form value? $\endgroup$ – clathratus May 2 at 16:42

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