4503.sagews

integrate(arctan(x),x)

\newcommand{\Bold}[1]{\mathbf{#1}}x \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right)

integrate(arctan(x),x,0,3^(1/2))

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{3} \, \pi \sqrt{3} - \frac{1}{2} \, \log\left(4\right)

integrate(1/(x^3+1),x)

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, {\left(2 \, x - 1\right)} \sqrt{3}\right) + \frac{1}{3} \, \log\left(x + 1\right) - \frac{1}{6} \, \log\left(x^{2} - x + 1\right)

integrate(x^3*(9-x^2)^(1/2),x)

-1/5*(-x^2 + 9)^(3/2)*x^2 - 6/5*(-x^2 + 9)^(3/2)