x⁴⁹ ⁻¹ (x⁵⁰ ) (1+x¹⁰⁰ ) d x=k ( ⁻¹ (x⁵⁰ ) )^2+c , then k is equal to

Step-by-step solution

Let I= x⁴⁹ ⁻¹ (x⁵⁰ ) 1+ (x⁵⁰ )^2 d x Let x⁵⁰=t 50 x⁴⁹ d x=d t I= 1 50 ⁻¹ t 1+t^2 d t Let ⁻¹ t=u 1 1+t^2 d t=d u aligned I & = 1 50 u d u= u^2 100 +c & = ( ⁻¹ x⁵⁰ )^2 100 +c aligned But I=k ( ⁻¹ x⁵⁰ )^2+c (given) array rlrl & k ( ⁻¹ x⁵⁰ )^2+c & = 1 100 ( ⁻¹ x⁵⁰ )^2+c & & k & = 1 100 array