Question

`int (cos x + x sin x)/(x^2 + x cos x)`dx = ______.

विकल्प

• `log |(x sin x)/(x + cos x)| + "c"`

• `log |x/(x + cos x)| + "c"`

• log |cos x + x sin x| + c

• log|x² + x cos x| + c

Answer 1

`int (cos x + x sin x)/(x^2 + x cos x)`dx = `underline(log |x/(x + cos x)| + "c")`.

Explanation:

`int (cos x + x sin x)/(x^2 + x cos x)`dx

`= int (cos x + x sin x + x - x)/(x(x + cos x))`dx

`= int ((cos x + x) + x(sin x - 1))/(x (x + cos x))`dx

`= int 1/x  "dx" + int(sin x - 1)/(x + cos x)`dx

= log |x| - log(x + cos x) + c

= `log |x/(x + cos x)| + "c"`