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integral of (cosec(x))^1/2

integral of (cosec(x))^1/2

Grade:12

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

Dear priya,

To integrate cosec^n(x) and sec^n(x) you should seek "reduction
formulae" that is to say, reduce n by integration by parts until you get
down to something you recognize:

  int sec^2(x) = tan(x)

    int sec(x) = log|sec(x) + tan(x)|

               = log|tan(x/2 + pi/4)|

int cosec^2(x) = -cot(x)

  int cosec(x) = log|tan(x/2)|

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Sagar Singh

B.Tech IIT Delhi



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