Frequently Asked Questions
When should I complete the square?
When the denominator is an irreducible quadratic (negative discriminant) and the numerator is a constant. For factorable quadratics, partial fractions are usually faster.
Why arctan or natural log?
After completing the square the integral matches one of two standard forms: an integral of 1 over (u squared plus k) which gives arctan, or 1 over (u squared minus k) which gives a natural log via partial fractions.
What if the numerator is not a constant?
Split the numerator into a multiple of the derivative of the denominator (which integrates to natural log) plus a constant. The constant part uses this tool.
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This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.