If $f\left( x \right) = \cos \,\,x - {\cos ^2}\,\,x\,\, + \,\,{\cos ^3}\,\,x - \,\,.\,..\infty $, then $\smallint f\left( x \right)dx$ equals

$x\,\, - \,\,\frac{1}{2}\tan \,\,\frac{x}{2} + c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

f\left( x \right) = \cos \,\,x - {\cos ^2}\,\,x\,\, + \,\,{\cos ^3}\,\,x - \,\,.\,..\infty

, then

\int f\left( x \right)dx

equals

View answer and explanation

Correct option: D

x\,\, - \,\,\tan \,\,\frac{x}{2} + c

Option D (

x - \tan \frac{x}{2} + c

) is correct because it is the result of integrating the simplified trigonometric series.