Question
Mathematics Question on Relations and functions
If ∫x2+1x(x+1)2dx=Aln|x|+B1+x+C, where C is the constant of integration, then A+B =
A
(A) 5
B
(B) 4
C
(C) 3
D
(D) 2
Answer
(C) 3
Explanation
Solution
Explanation:
Given:∫x2+1x(x+1)2dx=Aln|x|+B1+x+C∫x2+1x(x+1)2=∫(x+1)2−2xx(x+1)2=∫(1x−2(1+x)2dx)=ln|x|−2(1+x)−1−1+C=ln|x|+21+x+CComparing with the RHS,A=1,B=2∴A+B=3.Hence, the correct option is (C).