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What is the integration of $\cot 4x \cos3x$?

I used many identities such as integration by parts, trigonometric identities, but could not come to any conclusion. Please help...

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    Oh shoot. That was a $\cot$.... – 2017-02-26
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    $\dfrac{\ln\left(\left|2\cos\left(x\right)+\sqrt{2}\right|\right)-\ln\left(\left|2\cos\left(x\right)-\sqrt{2}\right|\right)}{2^\frac{5}{2}}+\dfrac{-3\ln\left(\cos\left(x\right)+1\right)+3\ln\left(1-\cos\left(x\right)\right)+8\cos\left(3x\right)}{24}$ I cheated and used the online integrator. In my defence it's nasty though. – 2017-02-26
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    Can u provide me with step by step solution – 2017-02-26
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    Or at least starting approach of solving the ques – 2017-02-26
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    Type in into the online integrator it does the hard work and shows you the steps. Be warned there are lots of steps. Perhaps there is a smarter way that someone will provide? – 2017-02-26
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    @Moo Hm, fourth roots of negative one.... – 2017-02-26
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    Due to the $\ln$ being present, I would suggest a partial fraction decomposition. – 2017-02-26

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Hint...$$\frac{\cos 4x\cos 3x}{\sin 4x}=\frac{\cos4x\cos3x+\sin4x\sin3x}{\sin 4x}-\sin3x$$

$$=\frac{\cos x}{2\sin 2x\cos 2x}-\sin3x=\frac{1}{4\sin x\cos2x}-\sin 3x$$

$$=\frac{\sin x}{4(1-\cos^2x)(2\cos^2x-1)}-\sin 3x$$

Now use a substitution and partial fractions....