The value of ∫etan-1x1+x+x21+x2dx is
tan-1x+c
etan-1x+2x+c
etan-1x+c
etan-1x-x+c
xetan-1x+c
Explanation for the correct option:
Find the value of given integral.
Given:∫etan-1x1+x+x21+x2dx
∫etan-1x1+x+x21+x2dx=∫etan-1xx1+x2+1+x21+x2dx
=∫etan-1xx1+x2+1dx=∫etan-1xx1+x2+etan-1xdx=∫ddxxetan-1xdx
=xetan-1x+c, Where cis the integration constant.
Hence, option (E) is the correct answer.
The value of is
A. 1
B. 0
C. − 1
D.