# How do you integrate #int (2x-sinx) / (x^2 + cosx)#?

The numerator is the derivative of the denominator.

Use substitution:

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To integrate (\frac{{2x - \sin(x)}}{{x^2 + \cos(x)}}), you can use substitution method. Let (u = x^2 + \cos(x)), then (du = (2x - \sin(x))dx). The integral becomes (\int \frac{1}{u} du), which is (\ln|u| + C). Substitute back (u = x^2 + \cos(x)) to get the final answer: (\ln|x^2 + \cos(x)| + C).

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