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Can anyone solve this problem.Integration of ((tan x)^1/2)/(sin x cos x))

Can anyone solve this problem.Integration of ((tan x)^1/2)/(sin x cos x))

Grade:12

1 Answers

Avinash Kumar
36 Points
4 years ago
∫​((tan)^1/2)/(sinxcosx)=∫​sin-1/2xcos​-3/2​x dx
=multiply cos-1/2​x in numerator and denominator
=∫​(sin-1/2xcos​-2​x)/cos-1/2x dx
=∫​tan-1/2xsec2​x 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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