anonymous
  • anonymous
integrate csc^5 x dx
Mathematics
schrodinger
  • schrodinger
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.Sam.
  • .Sam.
http://www.chegg.com/homework-help/questions-and-answers/integral-csc-5-x-q47028
AravindG
  • AravindG
got it ?
TuringTest
  • TuringTest
\[\csc^2x=\cot^2x+1\]so\[\int\csc^5xdx=\int\csc x(\csc^4x)dx=\int\csc x(1+\cot^2x)^2dx\]this can be done from here using u-substitutions; remember that\[\frac d{dx}\csc x=-\csc x\cot x\]

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anonymous
  • anonymous
what happen next @TuringTest
TuringTest
  • TuringTest
expand and simplify\[\csc x(1+\cot^2x)^2\]what do you get?
anonymous
  • anonymous
csc x(1 + 2 cot^2 x + cot^4 x)
TuringTest
  • TuringTest
good, and distributing csc x...
TuringTest
  • TuringTest
oh dear, I really messed that up, never mind my original suggestion... your integral is actually pretty darn tricky, I will have to reevaluate my approach.

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