Can anyone solve this problem.Integration of ((tan x)^1/2)/(sin x cos x))
Aswath , 8 Years ago
Grade 12
Integral Calculus> Can anyone solve this problem.Integration...
1 Answers
Avinash Kumar
∫((tan)^1/2)/(sinxcosx)=∫sin-1/2xcos-3/2x dx
=multiply cos-1/2x in numerator and denominator
=∫(sin-1/2xcos-2x)/cos-1/2x dx
=∫tan-1/2xsec2x dx
now put tanx=u
du=sec2x dx
→ tan-1/2x=1/u1/2
= ∫du/u1/2 = 2u1/2 + C
= 2tan1/2x + C. Ans
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