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integralof1/square root of (sin^3x+cos^5X)

integralof1/square root of (sin^3x+cos^5X)

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
10 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

Thanks & Regards
Rinkoo Gupta
AskIITians faculty

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