Integrals Of Some Particular Functions

Let

I%3D%5Cint%20%5Cfrac%7B1%2B%5Clog%20x%7D%7B(1%2Bx%20%5Clog%20x)%5E%7B2%7D%7D%20d%20x

Let

1%2Bx%20%5Clog%20x%3Dt

%5CRightarrow%5Cleft(0%2Bx%20%5Ctimes%20%5Cfrac%7B1%7D%7Bx%7D%2B%5Clog%20x%5Cright)%20d%20x%3Dd%20t

%5CRightarrow%20(1%2B%5Clog%20x)%20d%20x%3Dd%20t

%5Ctherefore%20I%3D%5Cint%20%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%7D%20d%20t%3D%5Cfrac%7Bt%5E%7B-1%7D%7D%7B-1%7D%2BC

%3D%5Cfrac%7B-1%7D%7B(1%2Bx%20%5Clog%20x)%7D%2BC

Chapter Questions
1 MCQs