AngouriMath

Navigation

Home Quick start Wiki Almanac Research What's new Try Use Angouri.org GitHub Report a bug ~~Donate~~ Contacts

IntegrateAPowerTimesARadicalQuadratic(AngouriMath.Entity,AngouriMath.Entity,System.Int32,System.Int32,PeterO.Numbers.ERational,PeterO.Numbers.ERational)

Method (no overloads)

Summary

int y^m (A + c y^2)^(k/2) dy, written back in terms of
inTermsOf -- which is the variable itself where the quadratic had no
linear term, and the shifted variable where it did.

Remarks

Where the answer holds. Each of the three substitutions is a bijection only on
the interval where the radicand is positive, and that is where the integrand is real
in the first place: everywhere for A, c > 0, between the two roots for
c < 0, and outside them for A < 0. The answer is an antiderivative
on each such interval, which is the standing caveat on a trigonometric substitution
and is not something this writes as a condition.

AngouriMath

Table of contents

AngouriMath

IntegrateAPowerTimesARadicalQuadratic​(AngouriMath.​Entity,​AngouriMath.​Entity,​System.​Int32,​System.​Int32,​PeterO.​Numbers.​ERational,​PeterO.​Numbers.​ERational)

IntegrateAPowerTimesARadicalQuadratic(AngouriMath.Entity,AngouriMath.Entity,System.Int32,System.Int32,PeterO.Numbers.ERational,PeterO.Numbers.ERational)