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AP EAMCET2007MathematicsIndefinite Integration

x+8 x 4 x+6 x d x is equal to

Options

  1. Ax+ 1 2 (4 x+6 x)+c
  2. B2 x+ (2 x+3 x)+c
  3. Cx+2 (2 x+3 x)+c
  4. D1 2 (4 x+6 x)+c

Correct answer

A. x+ 1 2 (4 x+6 x)+c

Step-by-step solution

Let I= x+8 x 4 x+6 x d x We can write x+8 x=A(4 x+6 x)+B d d x (4 x+6 x) x+8 x=A(4 x+6 x)+B(4 x-6 x) On equating the coefficient of x and x , we get array ll 1=4 A-6 B, & 8=6 A+4 B & A=1, B= 1 2 array aligned I & = (4 x+6 x)+ 1 2 (4 x-6 x) 4 x+6 x d x & = (1+ 1 2 4 x-6 x 4 x+6 x ) d x & =x+ 1 2 (4 x+6 x)+c aligned

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