All Tasks
Integral
Calculate $\displaystyle \int \dfrac{1+x+x\sqrt{x^2+1}}{x^2+1}dx$
# Integrals of functions
Training
13
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