Thread: 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?

Nothing improper between the given limits:



Any problems with the anti-derivative?

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?

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.

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?

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