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Question
`int (cos x + x sin x)/(x^2 + x cos x)`dx = ______.
Options
`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
MCQ
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Solution
`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"`
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Integrals of Trignometric Functions
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