We have to find the integration of the following function
I tried but got stuck can anybody help me how to proceed . Is there anyother method to solve this 
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Koolman
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Is that$$\int\frac{n^2}{\left(n\sin n+\cos n\right)^2},\mathrm{d}n~~?$$Or is there a mix of $n$'s and $x$'s? – user170231 Jul 13 '16 at 18:42
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3Have a look here: http://math.stackexchange.com/questions/366509/evaluating-this-integral-small-int-frac-x2-dx-x-sin-x-cos-x2?noredirect=1&lq=1 – Olivier Oloa Jul 13 '16 at 18:43
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@user170231 in my question there no n only 'x' is present – Koolman Jul 13 '16 at 18:44
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1lab bhattacharjee answer is a nice way of working out this integral. – Jan Eerland Jul 13 '16 at 18:45
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@JanEerland i want to know how to proceed through my method – Koolman Jul 13 '16 at 18:52
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http://math.stackexchange.com/questions/1858507/method-of-integration – tired Aug 22 '16 at 11:15
1 Answers
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You have:
$\int \dfrac {x^2}{(x \sin x + \cos x)^2} dx\\ \int (x \sec x)\dfrac {x \cos x}{(x \sin x + \cos x)^2} dx$
How about integration by parts?
$u = x \sec x\\ dv \frac {x \cos x}{(x \sin x + \cos x)^2} dx$
Doug M
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1Your integral at the end. Multiply top and bottom by $\cos^2 x.$ Stuff cancels. Then you have a rather simple $\int sec^2 x dx$ – Doug M Jul 13 '16 at 19:16
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