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in Integrals calculus by (63.7k points)

Give reduction formula for ∫ cotn x dx.

1 Answer

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Best answer

Let In = ∫ cotn xdx 

 = ∫ cotn–2 x . cot2 x dx 

 = ∫ cotn–2 x .(cosec2 x – 1)dx 

 = ∫ cotn–2 x .cosec2 x dx – ∫ cotn–2 x dx 

 = – (cotn – 1x)/ (n – 1)) – In– 2 + C 

which is the required reduction formula.

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