Stuck in this problem: computing integral of arctan (1 - x + x^2 ), when evaluated between 0 and 1. Have been able to visualize how the area under the curve looks with a plot of arctan (...), which looks like something bounded between 0 and pi/4 on the y axis but unable to make progress on reducing the integral to a simple form. Appreciate. Stuck in this problem: computing integral of arctan (1 - x + x^2 ), when evaluated between 0 and 1. Have been able to visualize how the area under the curve looks with a plot of arctan (...), which looks like something bounded between 0 and pi/4 on the y axis but unable to make progress on reducing the integral to a simple form. Appreciate. @Mathematics

Question

Stuck in this problem: computing integral of arctan (1 - x + x^2 ), when evaluated between 0 and 1. Have been able to visualize how the area under the curve looks with a plot of arctan (...), which looks like something bounded between 0 and pi/4 on the y axis but unable to make progress on reducing the integral to a simple form. Appreciate.  Stuck in this problem: computing integral of arctan (1 - x + x^2 ), when evaluated between 0 and 1. Have been able to visualize how the area under the curve looks with a plot of arctan (...), which looks like something bounded between 0 and pi/4 on the y axis but unable to make progress on reducing the integral to a simple form. Appreciate.  @Mathematics

zarkon · Answer

try integration by parts

zarkon · Answer

$$u=\arctan(1-x+x^2),\hspace{1cm} dv=dx$$

anonymous · Answer

OK, makes sense, thanks Zarkon.