Can contour integration always be used to solve integrals?

[secret2]

I am trying to do the integration

\int_{0}^\infty \frac{x}{(x^2+c^2)^3} dx


At first I tried doing it with contour integration, but yielded zero. Later I figured out that it can actually be done simply by making a change in variable (squeezing the x in the numerator into the dx). Is it possible to do it with contour integration (though not necessary)?

 

[dextercioby]

I am trying to do the integration

\int_{0}^\infty \frac{x}{(x^2+c^2)^3} dx


At first I tried doing it with contour integration, but yielded zero. Later I figured out that it can actually be done simply by making a change in variable (squeezing the x in the numerator into the dx). Is it possible to do it with contour integration (though not necessary)?

Since it doesn't have real poles (thre denominator does not cancel in R),why didn't u try to do it only by the obvious substitution.I'm sure the result will not be awkward.

Daniel.

 

[M98Ranger]

It is not always possible to solve an integral using contour integration. In fact, contour integration is a powerful technique that can be used to evaluate many complex integrals, but it is not always the most efficient method. In this case, it may be easier to make a change of variable to solve the integral rather than using contour integration. However, it is always good to explore different methods and techniques when solving integrals, as it can help to deepen our understanding of the problem and potentially provide alternative solutions. So while it may not be necessary in this case, it is always beneficial to try out different approaches.