AngouriMath
IntegrateLinearOverQuadratic(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
∫ (px + q)/(ax^2 + bx + c) dx, by writing the numerator as a multiple of the
denominator's derivative plus a constant:
px + q = (p/2a)(2ax + b) + (q - pb/2a). The first part integrates to a logarithm
and the second is the constant-numerator case above.
denominator's derivative plus a constant:
px + q = (p/2a)(2ax + b) + (q - pb/2a). The first part integrates to a logarithm
and the second is the constant-numerator case above.
Remarks
With a a symbol the constant-numerator case is a piecewise with an arm for
a = 0 , and on that arm the multiple of the derivative, which divided by
a , is not the integrand's: there it is (px + q)/(bx + c) , which is
px/b + (q - pc/b) ln(bx + c)/b . Timofeev's (b1 + c1 x)/(a + 2b x + c x^2) had no antiderivative, with the arm declined for the symbol in front.
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