IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

computer001

rootof{ (x+1/x)^2 + 2(x+1/x)-3 } -log[x+1/x + rootof{ (x+1/x)^2 + 2(x+1/x)-3}] -sin(inverse){ (x+ 1/x +5)/(x + 1/x +2)}

computer001

inside the root devide by x n take the x out ,multiply numerator n denominator by (1+x) and bring it to t=x+1/x...
u will get integral [root of{(t-1)(t+3)}]dt/t+2

after tht direct

elastiboysai

Fantastic Gokul

But can u show the working

Im afraid not Evry1 wuld understand wat u meant.

computer001

im not able 2 use the editor stuff.. so il scan it n put it??

elastiboysai

k sure

computer001

here goes..

computer001

Re:Integrals challenge 2

konichiwa2x

The radicand is

the integral can be written as

.

Make the substitution

and it becomes

.

Next substitution,

, leads to

.

This can be converted into the integral of a rational function by yet another substitution

. It gives

. I

You can now split that into partial fractions and integrate it without further difficulties to get the answer.

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