Doubt on integration

hard
indefinite-integration
sm
trigonometry
unsolved
#1

Screenshot_20190817-165332

#2

Please provide the complete solution

#3

very easy way is make the denominator as (sinx+cosx)^2

sinx=(sinx+cosx)^2-1/2

add and subtract cosx in numerator
then very easy.. @Akash_2 sir

#4

I still don't understand, could you please write the expansion what you are saying?
@Sneha_2021

#5

ignore post 3 i have done little mistake just thinking in my mind sorry @akash_2 sir...

1 Like
#6

No problem dear, but still good efforts.
@Sneha_2021

#7

Just write sin2x as 2sinxcosx then convert all sinx and cosx into a tan (x/2). Then assume tan(x/2)=u and differentiate it to get dx in terms of du. Convert all sec^2(x/2) into tan^2(x/2) by identity. Now you will get some polynomial/polynomial which can be solved by separating it easily...

#8

will not easy to tackle by ur method i have done that forming a cubic equation typical to solve...u may post solution if you did it thanks sir @Abhishek_2020_3..

#9

#10

I think changing all term to half angle will do something it can be turn into x⁴ equation

#11

Same equation will come out if we put cosx=t in intial stage

#12

I also tried by this method but could not reached to any Solution. If you can then please post the solution .

#14

Sir,please provide the whole solution as the polynomial formed in this is also not integrable by me.

#15

Okk sir, I am waiting for your solution.

#16

Sir can you please provide the answer of this question and also the source of question because I don't think it is an integrable function (within jee syllabus) according to me.

Still I think there should be a term of (ln(1+tan(x/2)))/8 in the answer...

1 Like
#17

Bro,I also don't have answer of this question this question was asked to me from one of my friend and it seems to be a good question so I post this solution here,but if I will get the answer of this question then I will definitely mention the answer.
Thanks for your efforts.

#20

It's solution is way too big

#21

https://www.integral-calculator.com you can get it from here.

#22

If you are unable to give the full solution, then please try to give the solution until we reach to the simpler form.

#23


Try solving in this form