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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.

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.
 A numerator that is a multiple of the derivative leaves no constant part, and the
arctangent it would have is left out rather than multiplied by zero, as the higher
powers leave it out: 0 * arctan(2x/2) is 0 only where the arctangent has
a value, so x/(x^2 + 1) was answered with provided not 1 + (2x/2)^2 = 0 once the arctangent's poles were in its condition, beside a logarithm that has none
there either. https://github.com/asc-community/AngouriMath/issues/2256

























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