AP EAMCET201920 Apr 2019Morning ShiftMathematicsIndefinite IntegrationActual
( x-1 (x+1) x^3+x^2+x d x= )
Options
- A(2 ⁻¹ ( 1+x+x^2 x )+c )
- B( ⁻¹ ( 1+x+x^2 x )+c )
- C( ⁻¹ ( x 1+x+x^2 )+c )
- D( ⁻¹ ( 1+x^2 x )+c )
Correct answer
A. (2 ⁻¹ ( 1+x+x^2 x )+c )
Step-by-step solution
( aligned & x-1 (x+1) x^3+x^2+x d x & = x^2-1 (x+1)^2 x 1+ 1 x +x d x & = x^2-1 (1+1+ 1 x +x ) x^2 1+ 1 x +x d x & = 1 [1+ (1+ 1 x +x ) ] 1+ 1 x +x d x aligned ) Let (1+ 1 x +x=t^2 ) ( aligned & (1- 1 x^2 ) d x=2 t d t= 2 t d t (1+t^2 ) t =2 d t 1+t^2 & =2 ⁻¹(t)+c=2 ⁻¹ ( 1+x+x^2 x )+C aligned ) Hence, option (1) is correct.