All Tasks - Asymptote

Indicate the logical value $$\displaystyle \int \dfrac{1+x}{x^2+1}~dx=\arctan(x)+\ln|x^2+1|+ C$$

Calculate $\displaystyle \int \dfrac{1+x+x\sqrt{x^2+1}}{x^2+1}dx$

The primitive function of $\int \frac{x^3}{\sqrt{x}}dx$ is:

Complete in order to obtain a true statement.

Using a suitable change of variable, we have that $$\int\frac{\sqrt[3]{(x^3-1)^6}}{x^{-2}}dx=\int\frac{u^2}{3}du$$ Indicate what was the change of variable made.

Using the change of variables $x=ln(u-1), u> 1$, the integral $$\int\frac{1}{e^x+1}dx$$ in the new variable is: