AP EAMCET201823 Apr 2018Evening ShiftMathematicsIndefinite IntegrationActual
x^2+1 [ (x^2+1 )-2 x ] x^4 d x=
Options
- A1 9 (1+ 1 x^2 )^ 3 2 [2-3 (1+ 1 x^2 ) +c
- B1 3 (1+ 1 x^2 )^ 1 2 [6- (1+ 1 x^2 )^2 ]+c
- C1 9 (1+ 1 x^2 ) [3-2 (1+ 1 x^2 )^ 1 2 ]+c
- D1 3 (1+ 1 x^2 )^ 3 2 [3+ (1+ 1 x^2 ) ]+c
Correct answer
A. 1 9 (1+ 1 x^2 )^ 3 2 [2-3 (1+ 1 x^2 ) +c
Step-by-step solution
array r I= x^2+1 [ (x^2+1 )-2 x ] x^4 d x = 1 x^3 1+ 1 x^2 (1+ 1 x^2 ) d x array Let 1+ 1 x^2 =t^2 -2 d x x^3 =2 t d t So, I=- t^2 t^2 d t =-2 t^2 t d t=-2 [ t^3 3 t- ( t^3 3 1 t ) d t ] =- 2 3 t^3 t+ 2 9 t^3+c= 1 9 t^3 [2-3 t^2 ]+c = 1 9 (1+ 1 x^2 )^ 3 / 2 [2-3 (1+ 1 x^2 ) ]+c