$x^3\sin x + x^2\cos x - 6x\sin x + 6\cos x + c$

$x^3\sin x + 3x^2\sin x - 6x\sin x - 6\cos x + c$

$x^3\sin x + 3x^2\cos x - 6x\sin x - 6\cos x + c$

$x^3\sin x + 3x^2\cos x - 6x\sin x + 6\cos x + c$

$\log uv + c$

$\log\dfrac{u}{v} + c$

$\dfrac{v^2}{2u^2} + c$

$\dfrac{u^2}{2v^2} + c$

$\dfrac{-1}{2\tan x} + \dfrac{1}{2\sqrt{2}}\tan^{-1}\left(\dfrac{\tan x}{\sqrt{2}}\right) + c$

$\dfrac{-1}{2\tan x} - \dfrac{1}{2\sqrt{2}}\tan^{-1}\left(\dfrac{\tan x}{\sqrt{2}}\right) + c$

$\dfrac{1}{2\tan x} - \dfrac{1}{2\sqrt{2}}\tan^{-1}\left(\dfrac{\tan x}{\sqrt{2}}\right) + c$

$\dfrac{1}{2\tan x} + \dfrac{1}{2\sqrt{2}}\tan^{-1}\left(\dfrac{\tan x}{\sqrt{2}}\right) + c$

$\left(1 + \dfrac{1}{x^2}\right)^{3/2}\left[\dfrac{-1}{3}\log\left(1 + \dfrac{1}{x^2}\right) + \dfrac{2}{9}\right] + c$

$\left(1 + \dfrac{1}{x^2}\right)^{3/2}\left[\dfrac{-1}{3}\log\left(1 + \dfrac{1}{x^2}\right) - \dfrac{2}{9}\right] + c$

$\left(1 + \dfrac{1}{x^2}\right)^{3/2}\left[\dfrac{-1}{3}\log\left(1 + \dfrac{1}{x^2}\right) + \dfrac{2}{3}\right] + c$

$\left(1 + \dfrac{1}{x^2}\right)^{3/2}\left[\dfrac{-1}{3}\log\left(1 + \dfrac{1}{x^2}\right) - \dfrac{2}{3}\right] + c$