Editing Lists of integrals (section)

===Integrals with a singularity===
When there is a [[Singularity (mathematics)|singularity]] in the function being integrated such that the antiderivative becomes undefined at some point (the singularity), then ''C'' does not need to be the same on both sides of the singularity. The forms below normally assume the [[Cauchy principal value]] around a singularity in the value of ''C'', but this is not necessary in general. For instance, in
<math display="block">\int {1 \over x}\,dx = \ln \left|x \right| + C</math>
there is a singularity at 0 and the [[antiderivative]] becomes infinite there. If the integral above were to be used to compute a definite integral between −1 and 1, one would get the wrong answer 0. This however is the Cauchy principal value of the integral around the singularity. If the integration is done in the complex plane the result depends on the path around the origin, in this case the singularity contributes −''i''{{pi}} when using a path above the origin and ''i''{{pi}} for a path below the origin. A function on the real line could use a completely different value of ''C'' on either side of the origin as in:<ref>[[Serge Lang]] . ''A First Course in Calculus'', 5th edition, p. 290</ref>
<math display="block"> \int {1 \over x}\,dx = \ln|x| + \begin{cases} A & \text{if }x>0; \\ B & \text{if }x < 0. \end{cases} </math>