Interchanging Integral and Summation signs

Question

So, I know there are a few functions that don't have elementary antiderivatives, and the way I approach some of these problems is by integrating the Taylor series. In the process, I usually interchange the (indefinite) integral sign and the summation sign. Example: $$ \int \sin(x)/x\ dx\,=\\\int \sum_{n=0}^\infty (-1)^nx^{2n}/(2n+1)!\ dx=\\\sum_{n=0}^\infty ((-1)^{n}/(2n+1)!)\int x^{2n} dx=\\C+\sum_{n=0}^\infty (-1)^{n}x^{2n+1}/((2n+1)!(2n+1)) $$ Is this valid? when doing indefinite integrals of this sort (integrating Taylor series), when, if ever, will it be invalid to interchange the integration and summation signs?