Given that 3 x+4 x 2 x+5 x d x= x 29 + 29 |2 x+5 x|+c What is the value of ?

Step-by-step solution

Let, aligned & I = 3 x+4 x 2 x+5 x d x & 3 x+4 x= A (2 x+5 x) & + B [ d d x (2 x+5 x) ] & 3 x+4 x= A (2 x+5 x) & + B (-2 x+5 x) aligned Comparing co-efficient of x and x aligned & 3=2 A+5 B ....(i) & 4=5 A-2 B ....(ii) aligned Solving (i) and (ii) then we get, aligned & A = 26 29 , ~B = 7 29 & I = 26 29 (2 x+5 x)+ 7 29 (-2 x+5 x) 2 x+5 x d x &= 26 29 d x+ 7 29 (-2 x+5 x) 2 x+5 x d x &= 26 29 x+ 7 29 In (2 x+5 x)+c & =26, =7[ [on comparing] aligned =7