MHT CET2012MathematicsIndefinite Integration
The value of (x²+1 ) x⁴+x²+1 d x is
Options
- A1 3 ⁻¹ x-1 / x 3 +C
- B1 2 3 (x-1 / x)- 3 (x-1 / x)+ 3 +C
- C⁻¹ ( x+1 / x 3 )+C
- D⁻¹ ( x-1 / x 3 )+C
Correct answer
A. 1 3 ⁻¹ x-1 / x 3 +C
Step-by-step solution
Let I= x²+1 x⁴+x²+1 d x aligned =& (1+ 1 x² ) x²+1+ 1 x² d x =& (1+ 1 x² ) (x- 1 x )²+( 3 )² d x =& d t ( 3 )²+t² [ let t=x- 1 x d t= (1+ 1 x² ) d x ] =& 1 3 ⁻¹ ( t 3 )+C =& 1 3 ⁻¹ 1 3 (x- 1 x ) +C aligned