Integrate $\int_{0}^{1}\cot(1-x+x^2)\,\mathrm{d}x$

Question

I don't know how to compute this integral:

$$\int_{0}^{1}\cot^{-1}(1-x+x^2)\,\mathrm{d}x $$

Could somebody provide me with a hint?

Note: $\cot^{-1}(x)$ is the $\text{arccot}$ function.

Like your previous posts, you have uploaded an image instead of a latex formula. This not pleasure for people here! — Nosrati, Mar 19 '17 at 11:35
This has definitely been asked before in one way or another. — StubbornAtom, Mar 19 '17 at 12:25

score 7 · Accepted Answer · edited Mar 19 '17 at 12:13

7

Hint $\operatorname{arccot} (1-x+x^2)=\arctan (x)-\arctan (x-1) $ . Now use by parts separately on each function to get the answer.

edited Mar 19 '17 at 12:13

answered Mar 19 '17 at 12:13

Archis Welankar

Nicely done! :D – Simply Beautiful Art Mar 19 '17 at 12:14
not op, but thanks! Was just about to ask if this method was correct – math and physics forever Nov 24 '22 at 15:24

1 Answers1