$\displaystyle\int \dfrac{(x + 1)(x + \log x)^2}{x}\,dx =$

$\displaystyle\int \cot^4 x\,dx$ is equal to

$\displaystyle\int \dfrac{\cos^3 x}{\sin^2 x + \sin x}\,dx =$

$\displaystyle\int_{\pi/6}^{\pi/3} \dfrac{\sin x - \cos x}{1 + \sin x\cos x}\,dx =$