How to calculate $\int_{0}^{1} \frac{\log{(1+x)}}{x^{2}+1} \ dx $?

Question

$$\int_{0}^{1} \frac{\log{(1+x)}}{x^{2}+1} \ dx $$

I tried substituting x with 1/t but couldn't find the answer. Can someone provide any hint?

As many suggested I substituted x with tan t but again I got stuck at $$\int_{0}^{\frac{π}{4}} \log{(1+tant)} \ dt $$

I finally solved it and got the correct answer.

score -2 · Accepted Answer · answered Jan 21 '17 at 07:21

-2

Hint -

Put $\tan^{-1} x = t$

Then x = tan t.

And $\frac{1}{1 + x^2} dx = dt$

answered Jan 21 '17 at 07:21

Kanwaljit Singh

All downvotes are welcome. But please tell the reason so that I can improve my mistake. – Kanwaljit Singh Jan 21 '17 at 10:49
This is not a "good" question. Instead of posting an answer, you should encourage the person who posted the question to improve it. – Anne Bauval Jul 12 '23 at 16:04

score -2 · Answer 2 · answered Jan 21 '17 at 07:26

-2

Put $\displaystyle x = \frac{1-t}{1+t}$

answered Jan 21 '17 at 07:26

DXT

This is not a "good" question. Instead of posting an answer, you should encourage the person who posted the question to improve it. – Anne Bauval Jul 12 '23 at 16:04

2 Answers2