Q) \int ( \frac{1}{\sqrt[3]{x} + \sqrt[4]{x}} + \frac{ln( 1 + \sqrt[6]{x}}{\sqrt[3]{x} + \sqrt[]{x}} ) dx
23put x = t12
dx = 12t11dt
I=12\int [{}\frac{1}{t^{4}+t^{3}}+\frac{log(1+t^{2})}{t^{4}+t^{6}}]t^{11}dt
I=12\int [{}\frac{t^{8}}{t+1}+\frac{t^{7}log(1+t^{2})}{1+t^{2}}]dt
I_{1}=12\int {}\frac{t^{8}dt}{t+1}
I_{2}=12\int \frac{t^{7}log(1+t^{2})}{1+t^{2}}dt
log(1+t^{2})={m}, dm = \frac{2tdt}{1+t^{2}}
so,I_{2}=6\int \frac{t^{6}log(1+t^{2})2tdt}{1+t^{2}}=6\int (e^{m}-1)^{3}mdm
wich u can do further easily ,
BTW nishant sir , LAtex isnt working ....
1thanx qwerty...i started up similarly bt was messed up... isnt it a bit lenghthy!!!!
no other shorter tracks???
23donno there may be , but by looking at the problem u must instantly try to remove root signs , bcz then in the next steps u will get some idea of how to solve further
i think jee during those days was full of such lengthy sums