If 2 1+ x , dx = -4 (ax+b) + c , then the value of a, b respectively are...

Step-by-step solution

The given integral is 2 1+ x , dx . Using the trigonometric identity 1 + x = ( x 2 + x 2 )^2 , the integral becomes: 2 ( x 2 + x 2 ) , dx Integrating the terms, we get: 2 (-2 x 2 + 2 x 2 ) + c -2 2 ( x 2 - x 2 ) + c Multiplying and dividing the expression inside the parenthesis by 2 : -2 2 2 ( 1 2 x 2 - 1 2 x 2 ) + c -4 ( x 2 4 - x 2 4 ) + c Using the formula (A+B) = A B - A B : -4 ( x 2 + 4 ) + c Comparing this with the given expression -4 (ax+b) + c , we obtain: a = 1 2 , b = 4 Answer: 1 2 , 4