IIT JEE , AIEEE Forum - Mathematics , Integral Calculus - Integrals Challenge : rates for best answer

konichiwa2x

konichiwa2x

no takers?

studyid

hello this is really a good ques... yaar....

i have tried several times .. by several methods.... still not gettin it....

keep posting sums like this ...........

aditi_g

whrs the question yaar???? i cant get it on my screen??? how have u typed it??any spl spftware reqd for opening it??

studyid

hello aditi_g.......

if you are not clear with the ques....

the ques.. is..

integration of 1/(1+sinx + sin²x)

ziauddin75

hhey,it can be solved like this

_{[ ]}

^{[ ]} 1/(1+sinx)^2 --sinx d x

put sinx=t

_{[ ]}

^{[ ]} 1/ (

1-t^2)(t^2-1) dt

now you had got integrals of form

1/(p)(Q)

p is one and q is other quadratic eqn.

and solve it dude

if i'm correct ,then i'm going to post a questn from integrals try to solve

ziauddin75

solce this one

integrate 1/(a+btanx)^2 dx

konichiwa2x

no ziauddin75 , its not as simple as that. can you show your work?

anyway keep trying.

aditi_g , question is 1/(1+sinx + sin²x).

konichiwa2x

ziauddin75, is your question meant to be a challenge or a query? please make a new post.

ziauddin75

konichiva, i had left that question to stndrd integral type yaar,

dx/(a){(b)^.5}

a is quadratic,

b is quadratic,

you can solve further by

putting t=1/z and simplifying

then put

1+z^2=m^2 and got the answer.

qustn which i had given is my query but you can accept it as challenge too,it a tricky one ,cant solve easily,i had already posted it in coomunity q&a

ziauddin75

konic be fast in repyling,

konichiwa2x

no yaar, that method would work only if the expression was a quadratic in 'x'.

can you post your answer if you claim to have got it?

ziauddin75

t=1/z;
dt=-1/z^2
putting in previous eqn.
dt/(1-t^2)1/2 (t^-1)

-z^3/{z^2}{(z^-1)^1/2}{ (1-z^2)} dz
put z^2-1=k; 2zdz=dk
-1/2(dk/(k^1/2)*(-k)

1/2 i
i=dk/k^3/2 (integrate it and put the values)

hope now you can understand it
please rate me if i am correct

konichiwa2x

Quote from zuaddin15:

hhey,it can be solved like this
_{[ ]}^{[ ]} 1/(1+sinx)^2 --sinx d x

put sinx=t

_{[ ]}^{[ ]} 1/ (1-t^2)(t^2-1) dt

Ask & Discuss Questions with Community & Experts