If `int(1+xcosx)/(x(1-x^(2)e^(2sinx)))dx = k" ln "sqrt((x^(2)e^(2 sinx))/(1-x^(2)e^(2sinx)))+C` then k is equal to:

Explanation

To solve the integral

\[ \int \frac{1 + x \cos x}{x(1 - x^2 e^{2 \sin x})} \, dx, \]

we will follow the steps outlined in the video transcript.

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