# Require solution for this problem

$\large \int \dfrac x{1+ x \tan x} \, dx = \, ?$

Note by Aritra Jana
2 years, 4 months ago

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$\begin{eqnarray}&& \dfrac{ x}{1 + x\tan x} = \dfrac{x \cos x}{\cos x + x \sin x} = \dfrac{ (\cos x + x \sin x)'}{\cos x + x \sin x} = \dfrac d{dx} \ln (\cos x + x \sin x) \\ &&\Rightarrow \int \dfrac x{1 +x \tan x} \, dx = \ln (\cos x + x \sin x) + C \end{eqnarray}$

- 2 years, 4 months ago

How directly you had taken the differentiation on numerator ?

- 2 years, 3 months ago

Can you rephrase your question? I don't understand what you're saying.

- 2 years, 3 months ago