## All Tasks

#### Immediate integral

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

# Integration calculus

Training

13

#### Immediate integral

Complete in order to obtain a true statement.

# Integrals of functions

Training

13

#### Integral using variable change

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.

# Integration calculus

Training

13

#### Integral using variable change

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:

# Integration calculus

Training

13

#### Integral using variable change

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

# Integration calculus

Learning

13

#### Primitive concept

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

# Integration calculus

Reasoning

13