Methods Of Integration

Let

I%3D%5Cint%20%5Cfrac%7Bd%20x%7D%7Bx%20%5Csqrt%7Bx%5E%7B2%7D-a%5E%7B2%7D%7D%7D

Let,

x%3D%5Cfrac%7B1%7D%7Bt%7D

%5Ctherefore%20%5C%2C%20d%20x%20%3D-%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%7D%20%5C%2Cd%20t

%5Ctherefore%5C%2C%20I%20%3D%5Cint%20%5Cfrac%7B-d%20t%7D%7Bt%5E%7B2%7D%20%5Ccdot%20%5Cfrac%7B1%7D%7Bt%7D%20%5Csqrt%7B%5Cleft(%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%7D%5Cright)%5E%7B2%7D-a%5E%7B2%7D%7D%7D%3D-%5Cfrac%7B1%7D%7Ba%7D%20%5Cint%20%5Cfrac%7Bd%20t%7D%7B%5Csqrt%7B%5Cleft(%5Cfrac%7B1%7D%7Ba%7D%5Cright)%5E%7B2%7D-t%5E%7B2%7D%7D%7D

%3D-%5Cfrac%7B1%7D%7Ba%7D%20%5Csin%20%5E%7B-1%7D%20t%2BC%3D-%5Cfrac%7B1%7D%7Ba%7D%20%5Csin%20%5E%7B-1%7D%20%5Cfrac%7Ba%7D%7B%7Cx%7C%7D%2BC

%3DC-%5Cfrac%7B1%7D%7Ba%7D%20%5Csin%20%5E%7B-1%7D%20%5Cfrac%7Ba%7D%7B%7Cx%7C%7D

Chapter Questions
1 MCQs