₀^ / 2 x 3 x+ x d x=

Step-by-step solution

Let I= ₀^ / 2 x 3 x+ x d x Put x=A(3 x+ x)+B d d x (3 x+ x) = A (3 x + x )+ B (-3 x + x ) Thus 3 ~A + B =1 and A -3 ~B =0 Solving, we get B = 1 10 , ~A = 3 10 aligned & = 3 10 ₀^ 2 d x+ 1 10 ₀^ 2 d d x d x (3 x+ x) d x & = 3 10 [x]₀^ 2 + 1 10 [ |3 x+ x|]₀^ 2 & = 3 10 ( 2 )+ 1 10 [ |1|- |3|] & = 3 20 - 1 10 3 & aligned