# Thread: Is this an improper integral?

1. ## Is this an improper integral?

I have to integrate Int(-1,1)(x2 ln(x+5))dx

sorry for this way to write, but I didn't figure out the code to write it in proper form.

This integral is improper because it's not defined for x<=-5.

Is this true? How would you solve this integral in a fast way? I tried, but I always get stuck doing all the calculations. Can anyone give me some hint? Maybe there is a special way to solve integrals of this type?

2. ## Re: Is this an improper integral?

Nothing improper between the given limits:

Any problems with the anti-derivative?

3. ## Re: Is this an improper integral?

Originally Posted by infernalmich
I have to integrate Int(-1,1)(x2 ln(x+5))dx

sorry for this way to write, but I didn't figure out the code to write it in proper form.

This integral is improper because it's not defined for x<=-5.

Is this true? How would you solve this integral in a fast way? I tried, but I always get stuck doing all the calculations. Can anyone give me some hint? Maybe there is a special way to solve integrals of this type?
$\displaystyle \int_{-1}^1 x^2 \ln(x+5) \, dx$

if one of the limits of integration were x = -5 , then it would be improper.

as is, it's just a normal definite integral ... I would initially try integration by parts.

4. ## Re: Is this an improper integral?

Thank you for your help, now I remeber the definition that in order to be improper the indefinite values have to lie within the limits of integration.

Another try:
Int(1,2)(x/(12-x)1/3)dx

This integral is improper because it is not defined for 1, which is inside of the limit of integration.

In order to check if it is convergent, I set 1=b than I solve the integral and take its limit b->0+
The limit exists and is finite, therefore the integral converges. True?

5. ## Re: Is this an improper integral?

true ... if the limit exists (I did not check if it indeed does so)