I need to use

$\cot Q+\tan Q=2\csc 2Q$

to integrate

$$\int \csc 2Q\,\mathrm{d}Q.$$

the integral becomes $$\frac12\int\left(\frac{\cos Q}{\sin Q} + \frac{\sin Q}{\cos Q}\right)\,\mathrm{d}Q$$

Is it possible to use substitution, what are other methods?


1 Answer 1


Hint : The derivation of sinQ is cosQ and the derivation of cosQ is -sinQ. So you can solve the integral by two substitutions.

  • $\begingroup$ How do you turn $1/2[lnsqrt{3} - ln(1/sqrt{3})]$ to 1/2ln3 $\endgroup$
    – Arodi007
    Oct 21, 2014 at 20:34
  • 1
    $\begingroup$ @Arodi007 $\ln \sqrt{3} + \ln\frac{1}{\sqrt{3}} = \ln\sqrt{3} + \ln\sqrt{3} = \ln((\sqrt{3}\cdot\sqrt{3}) = \ln 3$. Note that $\ln x+\ln y=\ln(xy)$ and $-\ln x=\ln(1/x)$ hold. (Anyway, Kirino is so cute, isn't it?) $\endgroup$
    – Hanul Jeon
    Oct 21, 2014 at 23:32

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