# Indefinite Integral Doubt!

$\large I = \int\dfrac{\sqrt{cos(2x)}}{cosx} dx$

$Note$ : Anyone and everyone please post your solution , this question appeared in my class test.

Note by Rishu Jaar
3 years, 8 months ago

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$\dfrac{\sqrt{\cos 2x}}{\cos x} = \dfrac{\cos 2x}{\cos x \sqrt{\cos 2x}}$

$\dfrac{2\cos^2 x -1}{\cos x \sqrt{2\cos^2 x -1}} = \dfrac{2\cos x }{\sqrt{2\cos^2 x -1}}-\dfrac{1}{\cos x \sqrt{2\cos^2 x -1}}$

For first term setting $\sin x = u$ will convert it into a standard integral. For the second term first set $\sin x = u$ then then set $\dfrac{1}{t}=u$. This will convert it into a standard integral.

- 3 years, 8 months ago

Hey nice approach , thank you bro, i wonder if you are this good from self - study or do you go to some good coaching? $\ddot\smile$

- 3 years, 8 months ago

Self study. Although I have taken DLP from Resonance.

- 3 years, 8 months ago

Very nice , you joined any test series?

- 3 years, 8 months ago

Yes , Resonance.

- 3 years, 8 months ago

Oh that's great , what is your ranking (in around 8000 students i guess) , just curious , actually here in mathura , i joined only a local coaching(they were frauds) which was disastrous , and thus i want to check my level of preparedness.(i am not much confident)

- 3 years, 8 months ago

My average All resonance rank is around 150. Trying to improve this figure.

- 3 years, 8 months ago

Awesome rank bro, your best ? My best in PACE was APR 220 .

- 3 years, 8 months ago

My best is ARR 33.

- 3 years, 8 months ago

That's amazing , with ranks around those you can guarantee a top 1000 AIR in JEE for sure , i guess? Are you revising the course , i mean is your syllabus finished entirely?

- 3 years, 8 months ago

No, I do have some topics to be covered. Will finish them soon.

- 3 years, 8 months ago

Ok nice , Is the resonance DLP material enough or do you refer some books, what is your revision strategy?

- 3 years, 8 months ago

It was nice talking to you , please do share your strategy when you are free , or owing to privacy we could chat at slack if you want.

- 3 years, 8 months ago

Mayank , you must be revising as the final stage for JEE , Or do you have to complete some left course topics like me ? I would be very thankful to you if you share your stats. and strategy , so that i can analyze my self better.

- 3 years, 8 months ago

@Md Zuhair , @Mayank Singhal , guys any help?

- 3 years, 8 months ago

Let me try ... :)

- 3 years, 8 months ago