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anonymous
 one year ago
Integrate cot^5(x) csc^8(x)
anonymous
 one year ago
Integrate cot^5(x) csc^8(x)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\cot ^5x=\cot x \cot ^4x=\cot x \left( \cot ^2x \right)^2=\cot x \left( \csc ^2x1 \right)^2\] \[=\cot x \left( \csc ^4x2\csc ^2x+1 \right)\] \[\csc ^8x \left( \csc ^4x2\csc ^2x+1 \right)\cot x=\csc ^7x \left( \csc ^4x2\csc ^2x+1 \right)\left( \csc x \cot x \right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[=\left( \csc ^{11}x2\csc ^9x+\csc ^7x \right)\left( \csc x \cot x \right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much. How did you know to take out a cscxcotx and not csc^2x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you can do that way also. \[\csc ^6x \csc ^2x=(csc^2x)^3csc^2x=\left( \cot ^2x+1 \right)^3\csc ^2x\] \[(\cot ^6x+3\cot ^4x+3\cot ^2x+1)\csc ^2x\]
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