NDA2017MathematicsIndefinite IntegrationActual
( In x)⁻¹ d x- ( In x)⁻² d x is equal to
Options
- Ax( In x)⁻¹+c
- Bx( In x)⁻²+c
- Cx( In x)+c
- Dx( In x)^2+c
Correct answer
A. x( In x)⁻¹+c
Step-by-step solution
aligned & ( x)⁻¹ d x- ( x)⁻² d x & = [ 1 x - 1 ( x)^2 ] d x aligned aligned & Put n x = t x = e ^ t & dx = e ^ t . dt . aligned aligned & [ 1 x - 1 ( x )^2 ] dx = ( 1 t - 1 t ^2 ) e ^ t dt & = e ^ t ( 1 t - 1 t ^2 ) dt aligned aligned & = e ^ t ( 1 t - 1 t ^2 ) dt & = e ^ t t + c = x x + c aligned =x( x)⁻¹+c