$-\left(\dfrac{\sqrt{2}}{3}\tan^{-1}\dfrac{x}{\sqrt{2}} + \dfrac{\sqrt{5}}{3}\tan^{-1}\dfrac{x}{\sqrt{5}}\right) + c$, where c is the constant of integration

$\left(\dfrac{\sqrt{2}}{3}\tan^{-1}\dfrac{x}{\sqrt{2}} + \dfrac{\sqrt{5}}{3}\tan^{-1}\dfrac{x}{\sqrt{5}}\right) + c$, where c is the constant of integration

$\dfrac{\sqrt{2}}{3}\tan^{-1}\left(\dfrac{x}{\sqrt{2}}\right) - \dfrac{\sqrt{5}}{3}\tan^{-1}\left(\dfrac{x}{\sqrt{5}}\right) + c$, where c is the constant of integration

$-\dfrac{\sqrt{2}}{3}\tan^{-1}\left(\dfrac{x}{\sqrt{2}}\right) + \dfrac{\sqrt{5}}{3}\tan^{-1}\left(\dfrac{x}{\sqrt{5}}\right) + c$, where c is the constant of integration

$\cot x + \cot^2 x + c$, where c is the constant of integration

$\tan x - \cot x - 3x + c$, where c is the constant of integration

$2\sin^5 x + 2\cos^5 x + c$, where c is the constant of integration

$\sin^3 x + 2\cos^3 x + c$, where c is the constant of integration

$a\theta\tan^2\theta - a\tan\theta - a\theta + c$  $\left(\text{where } \theta = \tan^{-1}\left(\sqrt{\dfrac{x}{a}}\right)\right)$ and c is the constant of integration

$a\theta\tan^2\theta - a\tan\theta + a\theta + c$  $\left(\text{where } \theta = \tan^{-1}\left(\sqrt{\dfrac{x}{a}}\right)\right)$ and c is the constant of integration

$a\theta\tan^2\theta + a\tan\theta - a\theta + c$  $\left(\text{where } \theta = \tan^{-1}\left(\sqrt{\dfrac{x}{a}}\right)\right)$ and c is the constant of integration

$a\theta\tan^2\theta + a\tan\theta + a\theta + c$  $\left(\text{where } \theta = \tan^{-1}\left(\sqrt{\dfrac{x}{a}}\right)\right)$ and c is the constant of integration

$0$

$1$

$2$

$-1$