Integral Challenge!

Calculus Level 3

Given that f ( x ) = ∫ 1 x ln ⁡ t 1 + t d t \displaystyle f(x) = \int_1^x \dfrac{\ln t}{1+t} \, dt and f ( x ) + f ( 1 x ) = k ( ln ⁡ x ) 2 f(x) + f\left(\dfrac1x\right) = k (\ln x)^2 for some constant k k , find the value of k k .

1 1 1 3 \dfrac13 1 2 \dfrac12 1 4 \dfrac14

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Rahul Saxena by rahul saxena , 23, India

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2 solutions

Rahul Saxena
Dec 22, 2015

7 Helpful 0 Interesting 0 Brilliant 0 Confused
Shivang Gupta
Dec 23, 2015

I also did the question in the same way as you did. I also think this is the only solution for this problem.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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