All Tasks - Asymptote

Calculate $\displaystyle \int x~e^{-x}~dx$

The primitive function of $\int x^2\tan(x^3)dx$ is:

Determine the value of $f(1)$, knowing that $f(0)=1$ and that $f^{\prime}(x)=\dfrac{4x}{(2-x^2)^3} $. (Enter the value with to 2 decimal places)

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: