# Computing $\int {\dfrac{\csc^{2014}x-2014}{\cos^{2014}x} dx}$

I don't know how to compute:

$$\int {\dfrac{\csc^{2014}x-2014}{\cos^{2014}x} dx}$$

I have tried substituting $t=\tan ^{2} x$ but got nothing out of it. I know there's some trick involved, but can't figure it out.

Also, how does one frame such questions involving numbers like the current year, next year or previous year?

Is there a general theme to attack such problems?

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I guess they use the 'year' in such problems as a kind of a hidden hint, meaning 'obviously don't try calculating by hand, there's a trick to this' – Spine Feast Apr 27 '14 at 16:08
@DepeHb, sometimes substitutions are obvious to such 'tricky' questions... But I cannot see how something easy or clever or tricky can be done to solve this. Would be great to see awesome solutions to this question.. – Apurv Apr 27 '14 at 16:12
Is this a definite integral whose limits were omitted, or is it really an indefinite one? – apnorton Apr 27 '14 at 16:21
Probably about the best I could do is write it as a sum. – Mike Apr 27 '14 at 16:37
It can be seperable such that $$\frac{1}{2^{2014}}\int\frac{dx}{\sin^{2014}2x}-2014\int\frac{dx}{\cos^{2014}x}‌​$$ But ı dont know what it does? – guest Apr 27 '14 at 17:10

This question seems to examine you how to use well the $\sum$ sign.