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Differential Calculus

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8 Dec 2011 14:18:39 IST

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integral of cosec^3

Mathematics

integral of cosec^3

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Siddharth rastogi

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17 Dec 2011 22:09:41 IST

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$1\/8 (-csc^2(x\/2)-4 log(cos(x\/2))+4 log(sin(x\/2))+sec^2(x\/2))$

where csc is cosec

Bipin Dubey

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29 Jan 2012 18:50:38 IST

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$\int cosecx.cosec^2x.dx=\int \sqrt{cot^2x+1}.cosec^2x.dx$

$Put\; y=cotx,\; then\; dy=-cosec^2x.dx$

$Integral \; becomes \; \int \sqrt{y^2+1}(-dy)$

$=-\frac{1}{2}y\sqrt{y^2+1}-\frac{1}{2}log\left (\sqrt{y^2+1}+y \right )+c$

Back substitute y to get the answer

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