Question 85525
A(x) = f'(x)
{{{ int( arctan(x) , dx , 0 , pi/4)}}}
[u = arctan(x)
[du = dx/(1 + x^2)
[dv = dx
[v = x
{{{x*arctan(x) - int( x/(1 + x^2) , dx , 0 , pi/4)}}}
[u = 1 + x^2
[du = 2x dx
{{{x*arctan(x) - int( x/(u) , du/2x , 0 , pi/4)}}}
{{{x*arctan(x) - (1/2)*int( 1/(u) , du , 0 , pi/4)}}}
{{{x*arctan(x) - (1/2)*ln(u)}}} | {{{pi/4}}} / 0
{{{x*arctan(x) - (1/2)*ln(1 + x^2)}}} | {{{pi/4}}} / 0
(pi/4)(arctan(pi/4) - (1/2)ln(1 + pi^2/16)
Aprox. 0.2827