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Indefinite Integral Doubt!

Please help me solve the following Integral :

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

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

Note by Rishu Jaar
1 month 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.

Mayank Singhal - 1 month ago

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

Rishu Jaar - 1 month ago

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Self study. Although I have taken DLP from Resonance.

Mayank Singhal - 1 month ago

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@Mayank Singhal Very nice , you joined any test series?

Rishu Jaar - 1 month ago

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@Rishu Jaar Yes , Resonance.

Mayank Singhal - 1 month ago

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@Mayank Singhal 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.

Rishu Jaar - 1 month ago

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@Mayank Singhal 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)

Rishu Jaar - 1 month ago

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

Mayank Singhal - 1 month ago

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

Rishu Jaar - 1 month ago

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@Rishu Jaar My best is ARR 33.

Mayank Singhal - 1 month ago

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@Mayank Singhal 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?

Rishu Jaar - 1 month ago

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

Mayank Singhal - 1 month ago

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@Mayank Singhal 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.

Rishu Jaar - 4 weeks, 1 day ago

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

Rishu Jaar - 4 weeks, 1 day ago

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

Rishu Jaar - 1 month ago

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Let me try ... :)

Md Zuhair - 4 weeks, 1 day ago

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