Kalkylator för bestämda och oegentliga integraler

Kalkylatorn försöker beräkna bestämda integraler (dvs. med integrationsgränser), inklusive oegentliga, och visar stegen.

Enter a function:

Integrate with respect to:

Enter a lower limit:

If you need `-oo`, type -inf.

Enter an upper limit:

If you need `oo`, type inf.

Please write without any differentials such as `dx`, `dy` etc.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: calculate $$$\int_{-\infty}^{3}\left( \frac{\ln{\left(x \right)}}{x} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{\ln{\left(x \right)}}{x} d x}=\frac{\ln{\left(\left|{x}\right| \right)}^{2}}{2}$$$ (for steps, see indefinite integral calculator)

Since there is infinity in the lower bound, this is an improper integral of type 1.

To evaluate an integral over an interval, we use the Fundamental Theorem of Calculus. However, we need to use limit if an endpoint of the interval is special (infinite).

$$$\int_{-\infty}^{3}\left( \frac{\ln{\left(x \right)}}{x} \right)dx=\left(\frac{\ln{\left(\left|{x}\right| \right)}^{2}}{2}\right)|_{\left(x=3\right)}-\lim_{x \to -\infty}\left(\frac{\ln{\left(\left|{x}\right| \right)}^{2}}{2}\right)=-\infty$$$

Since the value of the integral is not finite, then it is divergent.

Answer: the integral is divergent.

Please try a new game Rotatly

Kalkylator för bestämda och oegentliga integraler

Beräkna bestämda och oegentliga integraler steg för steg

Solution