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If integration of [(cos^4 x)/(sin^3 x (sin^5 x+cos^5 x ))]dx= k[(tan^5 x +1)/(tan^5 x)]+c then k=?

If integration of [(cos^4 x)/(sin^3 x (sin^5 x+cos^5 x ))]dx= k[(tan^5 x +1)/(tan^5 x)]+c then k=?

Grade:12th pass

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:
If you simply differentiate the answer (right hand side), then you will get the integrand & by comparison you can find the value of k.
L =\frac{d}{dx}(\frac{k(tan^{5}(x)+1)}{tan^{5}(x)}+c) = \frac{d}{dx}(k(1+cot^{5}(x))+c)
L = 5cot^{4}(x).(-csc^{2}(x))
L = \frac{-5 cos^{4}(x)}{sin^{6}(x)}
L = \frac{-5 cos^{4}(x)}{sin^{3}(x)sin^{3}(x)}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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