99 Percentile Qs Bank for JEE MainMathematicsIndefinite Integration

If x^3 ~d x 1+x^2 = a (1+x^2 ) 1+x^2 + b 1+x^2 + c (where c is a constant of integration), then the value of 3 ab is

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Correct answer

B. -1

Step-by-step solution

aligned & Put 1+x^2= t ^2 & 2 x ~d x=2 t dt & x ~d x= t d t & x^3 ~d x 1+x^2 & = t ^2-1 t t d t & = ( t ^2-1 ) dt & = t ^3 3 - t + c & = (1+x^2 )^ 3 2 3 - 1+x^2 + c & = 1 3 (1+x^2 ) 1+x^2 - 1+x^2 + c aligned aligned & a= 1 3 , b=-1 & 3 a b=-1 aligned

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