How do you integrate $\int (\frac{1}{2}) csc π t cot π t d t$ $int(1/2)cscpitcotpitdt$ ?

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How do you integrate $\int (\frac{1}{2}) csc π t cot π t d t$ $int(1/2)cscpitcotpitdt$ ?

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Answer 1 · 2015-03-04T13:08:02

You can try first to change your functions as:
$csc (x) = \frac{1}{sin (x)}$ $csc(x)=1/sin(x)$ and
$cot (x) = \frac{cos (x)}{sin (x)}$ $cot(x)=cos(x)/sin(x)$
so you can write:
enter image source here
Where at the end you integrate ${sin}^{- 2} (π t)$ $sin^(-2)(pit)$ as $x^{- 2}$ $x^(-2)$ in a normal integral.

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How do you integrate $\int (\frac{1}{2}) csc π t cot π t d t$ $int(1/2)cscpitcotpitdt$ ?

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How do you integrate $\int (\frac{1}{2}) csc π t cot π t d t$ $int(1/2)cscpitcotpitdt$ ?