Indefinite Integral Doubt!

Please help me solve the following Integral :

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

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

Note by Rishu Jaar
1 year, 11 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

cos2xcosx=cos2xcosxcos2x\dfrac{\sqrt{\cos 2x}}{\cos x} = \dfrac{\cos 2x}{\cos x \sqrt{\cos 2x}}

2cos2x1cosx2cos2x1=2cosx2cos2x11cosx2cos2x1\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 sinx=u\sin x = u will convert it into a standard integral. For the second term first set sinx=u\sin x = u then then set 1t=u\dfrac{1}{t}=u. This will convert it into a standard integral.

A Former Brilliant Member - 1 year, 11 months ago

Log in to reply

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 year, 11 months ago

Log in to reply

Self study. Although I have taken DLP from Resonance.

A Former Brilliant Member - 1 year, 11 months ago

Log in to reply

@A Former Brilliant Member Very nice , you joined any test series?

Rishu Jaar - 1 year, 11 months ago

Log in to reply

@Rishu Jaar Yes , Resonance.

A Former Brilliant Member - 1 year, 11 months ago

Log in to reply

@A Former Brilliant Member 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 year, 11 months ago

Log in to reply

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

A Former Brilliant Member - 1 year, 11 months ago

Log in to reply

@A Former Brilliant Member Awesome rank bro, your best ? My best in PACE was APR 220 .

Rishu Jaar - 1 year, 11 months ago

Log in to reply

@Rishu Jaar My best is ARR 33.

A Former Brilliant Member - 1 year, 11 months ago

Log in to reply

@A Former Brilliant Member 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 year, 11 months ago

Log in to reply

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

A Former Brilliant Member - 1 year, 11 months ago

Log in to reply

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

Rishu Jaar - 1 year, 11 months ago

Log in to reply

@A Former Brilliant Member 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 - 1 year, 11 months ago

Log in to reply

@A Former Brilliant Member 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 year, 11 months ago

Log in to reply

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

Rishu Jaar - 1 year, 11 months ago

Log in to reply

Let me try ... :)

Md Zuhair - 1 year, 10 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...