MHT CET202121 Sep 2021Evening ShiftMathematicsIndefinite IntegrationActual
1 x^ 1 2 +x^ 1 3 d x=
Options
- Ax - [3] x + [6] x - | [6] x +1|+c
- B2 x -3 [3] x +6 [6] x -6 | [6] x +1|+c
- C2 x +3 [3] x +6 [6] x +6 | [6] x +1|+c
- Dx + [3] x + [6] x + | [6] x +1|+c
Correct answer
B. 2 x -3 [3] x +6 [6] x -6 | [6] x +1|+c
Step-by-step solution
Let I= d x x^ 1 2 +x^ 1 3 Put x^ 1 6 =t x=t^6 d x=6 t^5 dt. Also x^ 1 2 =t^3 and x^ 1 3 =t^2 aligned & I=6 t^5 d t t^2(1+t) & =6 t^3 (1+t) d t=6 (t^3+1 )-1 (1+t) =6 (t+1) (t^2-t+1 ) (1+t) d t-6 d t 1+t & =6 (t^2-t+1 ) d t-6 |1+t|+c= 6 t^3 3 - 6 t^2 2 +6 t-6[ |1+t|]+c & =2 x -3 [3] x +6 [6] x -6 |1+ [6] x |+c aligned