- #1
Raghav Gupta
- 1,011
- 76
Homework Statement
For x> 0 , let f(x) = $$\int _1^x \frac{log t dt }{1+t}$$
Then ## f(x) + f(1/x)## is equal to :
A. ##¼ (log x)^2 ##
B. ## ½ (log x)^2 ##
C. ##log x ##
D. ## ¼ log x^2 ##
Homework Equations
Suppose f(x) = $$\int _1^x g(t)$$
Then by Leibniz rule ,
f' (x) = g(x)
The Attempt at a Solution
I found f' (x) = logx/(1+x)
f' ( 1/x) = logx/x(x+1)
f' (x) + f'(1/x) = logx/x
Now what to do?
We can integrate both sides but a constant will appear which we don't know?