AP EAMCET20226 Jul 2022Morning ShiftMathematicsIndefinite IntegrationActual
1 ( x+ x+ 2 2 x )^2 d x=
Options
- A-(1+3 x ) (3+ ^2 x )^3 +C
- B-(1+3 x ) 3(1+ x )^3 +C
- C-(1+ x ) 3(1+3 x )^2 +C
- D1 (1+3 x )^3 +C
Correct answer
B. -(1+3 x ) 3(1+ x )^3 +C
Step-by-step solution
aligned & 1 ( x+ x+ 2 2 x )^2 d x & 1 ( x + x)^4 d x . = ^2 x ( x +1) d x aligned Let x=t^2 ^2 x d x=2 t d t aligned & 2 t (t+1) d t=2 ( 1 (t+1)^3 - 1 (t+1)^4 ) d t & =2 [ 1 3(t+1)^3 - 1 2(t+1)^2 ]+c & = -[3 t+1] 3(t+1)^3 +c= -(1+3 x ) 3(1+ x )^3 +c aligned