An infinite limit or singularity needs a convergence check, not just a very large finite bound.
Find it
Analyze → Improper integrals
Improper integrals expanded in the Analyze panel.Click to enlarge ↗
Try it step by step
Choose the explicit integrand.
Enter the lower and upper bounds; infinity and -infinity are accepted.
List known interior singularities when the chosen method provides that field.
Choose the integration method and calculate. Read the convergence explanation.
Examples to try
Each card is one input. For definitions, enter the cards in order. Formula-only cards belong in the tool described above.
Integrate this from 0 to infinity with absolute convergence; the result approaches 1.
Options explained
Absolute convergence
The standard mode for supported infinite tails and endpoint singularities. Known interior breaks are checked separately.
Cauchy principal value
Uses the supported symmetric limiting interpretation. A principal value can exist when the ordinary improper integral does not; report which one you calculated.
Alternating decaying tail
A specialized method for supported alternating tails. Supply the half-period width.
Interior singularities
List break locations such as 0 or 2 rather than allowing an interval to hide a pole.
Half-period width
For the alternating method, specify the distance between alternating half-waves.
Unresolved result
The tool can reject divergence or report that its bounded calculation did not establish convergence. Do not turn that message into zero.
