AngouriMath
IntegrateLinearOverPowerOfQuadratic(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,System.Int32,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
∫ (px + q)/(a x^2 + b x + c)^n dx, by the same rewrite of the numerator the single
power uses:px + q = (p/2a)(2ax + b) + (q - pb/2a) . The first part is the
denominator's own derivative over a power of it, which integrates as a power; the
second is the constant-numerator case above.
power uses:
denominator's own derivative over a power of it, which integrates as a power; the
second is the constant-numerator case above.
Remarks
A numerator that is already a multiple of that derivative leaves nothing of the
second part, and it is dropped rather than multiplied by zero. Multiplying is not
harmless: the reduction is a quotient by the quadratic, so0 * (2x/(x^2 + 1)) is 0 provided not 1 + x^2 = 0 and not 0 — correctly, since the factor
has no value there. Carrying that condition would attach it to the answer for
x/(x^2 + 1)^2 , which had none before and is owed none.
second part, and it is dropped rather than multiplied by zero. Multiplying is not
harmless: the reduction is a quotient by the quadratic, so
has no value there. Carrying that condition would attach it to the answer for
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