MHT CET202014 Oct 2020Evening ShiftMathematicsIndefinite IntegrationActual
[ 1- x 1+( x)² ]² d x=
Options
- A1 1+( x)² +c
- Bx 1+( x)² +c
- C1 1+ x +c
- Dx 1+ x +c
Correct answer
B. x 1+( x)² +c
Step-by-step solution
aligned Let I &= [ 1- x 1+( x)² ]² d x Put x &=t 1 x d x=d t d x=x dt i.e. d x=e^ t d t I &= e^ t [ 1-t 1+t² ]² d t= e^ t (1-t)² (1+t² )² d t= e^ t [ 1+t²-2 t (1+t² )² ] d t I &= e^ t [ 1 1+t² - 2 t (1+t² )² ] d t= e^ t 1+t² +c I &= x 1+( x)² +c aligned