JEE Main2013MathematicsIndefinite IntegrationActual

If the integral 8 x+1 2 x- 2 x d x=A 8 x+k where k is an arbitrary constant, then A is equal to:

Options

A- 1 16
B1 16
C1 8
D- 1 8

Correct answer

A. - 1 16

Step-by-step solution

Let I = 8 x+1 2 x- 2 x d x Now, D ^r= 2 x- 2 x= 2 x 2 x - 2 x 2 x = ^2 2 x- ^2 2 x 2 x 2 x = 2 4 x 4 x aligned I &= 2 ^2 4 x 2 4 x 4 x d x= 2 ^2 4 x 4 x 2 4 x d x &= 1 2 8 x d x=- 1 2 8 x 8 +k &=- 1 16 8 x+k & Now ,- 1 16 8 x+k= A 8 x+k & A =- 1 16 aligned

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