^2 , , ( , + , )^2 , ,d - Vidyadip

MCQ

$\int {{{\sec }^2}\theta } \,\,{(\sec \theta \, + \,\tan \theta )^2}\,\,d\theta $

A
$\frac{{(\sec \theta \, + \,\tan \theta )}}{2}\,[2\, + \,\tan \theta \,(\sec \theta \, + \,\tan \theta )]\,\, + \,\,C$
B
$\frac{{(\sec \theta \, + \,\tan \theta )}}{3}\,[2\, + \,4\tan \theta \,(\sec \theta \, + \,\tan \theta )]\,\, + \,\,C$
✓
$\frac{{(\sec \theta \, + \,\tan \theta )}}{3}\,[2\, + \,\tan \theta \,(\sec \theta \, + \,\tan \theta )]\,\, + \,\,C$
D
$\frac{{3\,(\sec \theta \, + \,\tan \theta )}}{2}\,[2\, + \,\tan \theta \,(\sec \theta \, + \,\tan \theta )]\,\, + \,\,C$

✓

Answer

Correct option: C.

$\frac{{(\sec \theta \, + \,\tan \theta )}}{3}\,[2\, + \,\tan \theta \,(\sec \theta \, + \,\tan \theta )]\,\, + \,\,C$

c
put $\sec\, \theta + \tan \, \theta = t$

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