All Tasks - Asymptote

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:

Using the change of variables $u=e^x$, the integral $$\int\frac{1}{e^x+1}dx$$ is:

Without solving the integral tell if the equality is true (T) or false (F) $\int \frac{\sin(x)}{cos^2(x)}dx=\sec(x)+C$

Without solving the integral tell if the equality is true (T) or false (F) $\int x\sin(x)dx=x \cos(x)-\sin(x)+C$