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Flag Integral Calculus> ∫dx/rootover(sin^3x.cos^5x)= 1.2/3((tan^2...
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∫dx/rootover(sin^3x.cos^5x)=1.2/3((tan^2x-1)/root tanx)+c2.2/3((tan^2x-2)/root tanx)+c3.2/3((tan^2x-3)/root tanx)+c4.2/3((tan^2x-4)/root tanx)+cplease solve this the answer is option 3please explain me the procedure

chandrika , 5 Years ago
Grade 12th pass
anser 1 Answers
Arun

Last Activity: 5 Years ago

Integral of 1/sqrt of (sin^3xcos^5x) dx
=integral of sec^4x dx/sqrt of tan^3x
let tanx=t
on differentiating w.r.to x we get
sec^2x dx=dt
integral of (1+t^2)/t^3/2 .dt
=integral {t^(-3/2) +t^(1/2)} dt
=t^(-1/2)/(-1/2) + t^(3/2)/(3/2)
=-2/sqrt t +2/3 .t^(3/2)
=-2/sqrt of tanx + 2/3(tanx)^3/2

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