Hey,
So, the original task was as follows: "Calculate the following generalized integral, or prove that it´s divergent.", and the integral itself was:
.
To define this indefinite integral I used limes x---> infinity, and changed the interval of the integral to 0,x.
After that, I factorized x^4+1 and used partial fraction decomposition, which led me to:
limes (x--->infinity):
And this I know I can split into two limits, with one fraction of the integral each. How to proceed henceforth is where I´m lost, though. Do you calculate the integral firstly, and limes secondly? Or the other way around? Because lim(x--->infinty) of both the integrals is obviously 0, and the primitive function of 0 is just an unknown number C, right? And if I have to calculate the integrals before the limit value, how would I do that?
Really grateful for answers!
So, the original task was as follows: "Calculate the following generalized integral, or prove that it´s divergent.", and the integral itself was:
To define this indefinite integral I used limes x---> infinity, and changed the interval of the integral to 0,x.
After that, I factorized x^4+1 and used partial fraction decomposition, which led me to:
limes (x--->infinity):
And this I know I can split into two limits, with one fraction of the integral each. How to proceed henceforth is where I´m lost, though. Do you calculate the integral firstly, and limes secondly? Or the other way around? Because lim(x--->infinty) of both the integrals is obviously 0, and the primitive function of 0 is just an unknown number C, right? And if I have to calculate the integrals before the limit value, how would I do that?
Really grateful for answers!