∫13sin⁡x+cos⁡xdx=12∫132sin⁡x+12cos⁡xdx=12∫1sin⁡x+π6dx=12∫cosec⁡x+π6dx=12loge⁡tan⁡x2+π12+c

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

$\int \frac{1}{\sqrt{3} \sin x + \cos x} d x .$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$\frac{1}{2} \log |T a n (\frac{x}{2} + \frac{5 π}{12})| + C$

$\frac{1}{2} \log |T a n (\frac{x}{2} + \frac{3 π}{4})| + C$

$\frac{1}{2} \log |T a n (\frac{x}{2} + \frac{5 π}{12}) + C$

$\frac{1}{2} \log |T a n (\frac{x}{2} + \frac{π}{12}) + C$

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} \int \frac{1}{\sqrt{3} \sin x + \cos x} d x \\ = \frac{1}{2} \int \frac{1}{\frac{\sqrt{3}}{2} \sin x + \frac{1}{2} \cos x} d x \\ = \frac{1}{2} \int \frac{1}{\sin (x + \frac{π}{6})} d x \\ = \frac{1}{2} \int cosec (x + \frac{π}{6}) d x \\ = \frac{1}{2} \log_{e} |\tan (\frac{x}{2} + \frac{π}{12})| + c \end{array}$