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∫ tan^-1(secx+tanx)dx

∫ tan^-1(secx+tanx)dx

Grade:

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
integral tan^-1(1+sinx)/cosx dx
=integral tan^-1(sin^(x/2)+cos^(x/2)+2sin(x/2)cos(x/2))/(cos^(x/2)-sin^(x/2)) dx
=integral tan^-1[{cos(x/2)+sin(x/2)}^2/(cos(x/2)-sin(x/2)).(cos(x/2)+sin(x/2)) dx
=integral tan^-1[(cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2))dx
=integral tan^-1(1+tan(x/2))/(1-tan(x/2)) dx
=integral tan^-1{tan(pi/4)+tan(x/2)}/(1-tan(pi/4).tan(x/2)) dx
=integral tan^-1tan(pi/4+x/2) dx
=integral (pi/4+x/2) dx
=pi.x/4+x^2/4 Ans.
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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