AngouriMath
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IntegrateRootOfQuadratic(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
The antiderivative of sqrt(a x^2 + b x + c) :
(2ax + b) sqrt(Q) / (4a) + ((4ac - b^2) / (8a)) times the integral of
1/sqrt(Q) -- integration by parts once, leaving the reciprocal form that
IntegrateOverRootOfQuadratic(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable) already knows.
IntegrateOverRootOfQuadratic(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable) already knows.
Remarks
Only where the leading coefficient is a number other than zero. With a = 0 this
is the square root of something linear, which the ordinary power rule already
integrates, and dividing by a would not be allowed anyway.
is the square root of something linear, which the ordinary power rule already
integrates, and dividing by a would not be allowed anyway.
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