please help me find: limit, x-> infty, int[pi/4, x] (arctan(t))^2 dt/ sqrt(x^2+1)

[daniel_t]

Can you please help me to find this limit?

. . . . .\(\displaystyle \large \displaystyle \lim_{x\, \rightarrow\, \infty}\, \)\(\displaystyle \large \displaystyle \dfrac{\left(\,\int\limits_{\frac{\pi}{4}}^{x}\, \left(\arctan(t)\right)^2\, dt\, \right)}{\sqrt{\strut x^2\, +\, 1\,}}\)

 

[Steven G]

Can you please help me to find this limit?

. . . . .\(\displaystyle \large \displaystyle \lim_{x\, \rightarrow\, \infty}\, \)\(\displaystyle \large \displaystyle \dfrac{\left(\,\int\limits_{\frac{\pi}{4}}^{x}\, \left(\arctan(t)\right)^2\, dt\, \right)}{\sqrt{\strut x^2\, +\, 1\,}}\)

Sure we can help you. What have you done so far. Show us your work and we will help you by showing you where you made an error, etc. Can you solve the integral?