AP EAMCET202422 May 2024Evening ShiftMathematicsIndefinite IntegrationActual
e^ 4 x^2+8 x-4 (x+1) (3 x^2+6 x-4 ) d x=
Options
- Ae^ 4 x^2+8 x-4 25 [3 (3 x^2+6 x-4 )-4 (3 x^2+6 x-4 ) ]+c
- Be^ 4 x^2+8 x-4 50 [4 (3 x^2+6 x-4 )+3 (3 x^2+6 x-4 ) ]+c
- Ce^ 4 x^2+8 x-4 25 [3 (3 x^2+6 x-4 )+4 (3 x^2+6 x-4 ) ]+c
- De^ 4 x^2+8 x-4 50 [4 (3 x^2+6 x-4 )-3 (3 x^2+6 x-4 ) ]+c
Correct answer
B. e^ 4 x^2+8 x-4 50 [4 (3 x^2+6 x-4 )+3 (3 x^2+6 x-4 ) ]+c
Step-by-step solution
I= e^ 4 x^2+8 x-4 (x+1) (3 x^2+6 x-4 ) d x Let x^2+2 x=t (x+1) d x= d t 2 I= 1 2 e^ 4 t-4 (3 t-4) d t We know, e^ a x (b x+c) d x= e^ a x a^2+b^2 (a (b x+c)+b (b x+c)) aligned & I= 1 2 e^ 4 t-4 16+9 (4 (3 t-4)+3 (3 t-4))+c & I= e^ 4 x^2+8 x-2 50 [4 (3 x^2+6 x-4 )+3 (3 x^2+6 x-4 ) ]+c aligned