If I= ₀^ / 2 d x 5+3 x = ⁻¹ ( 1 2 ) , then =

Step-by-step solution

Given, I= ₀^ / 2 d x 5+3 x = ⁻¹ ( 1 2 ) Now, I= ₀^ / 2 d x 5+3 x aligned & = ₀^ / 2 d x 5+3 2 x / 2 1+ ^2 x / 2 & = ₀^ / 2 .d put x= 2 x / 2 1+ ^2 x / 2 ] 5+5 ^2 x / 2+6 x / 2 1+ ^2 x / 2 & = ₀^ / 2 (1+ ^2 x / 2 ) d x 5+5 ^2 x / 2+6 x / 2 I & = ₀^ / 2 ^2 x / 2 d x 5+5 ^2 x / 2+6 x / 2 aligned On putting x 2 =t 1 2 ^2 x 2 d x=d t When x= 2 t=1 and x=0 t=0 , we get I= ₀^1 2 d t 5+5 t^2+6 t aligned & = 2 5 ₀^1 d t 1+t^2+ 6 5 t & = 2 5 ₀^1 d t (t^2+2 ( 3 5 ) t+ 9 25 )+1- 9 25 & = 2 5 ₀^1 d t (t+ 3 5 )^2+ 16 25 & = 2 5