: Mathématiques: quadratic integral

mathematical analysis > calculus > integral calculus > quadratic integral

quadratic integral

In mathematics, a quadratic integral is an integral of the form
${\\displaystyle \\int {\ rac {dx}{a+bx+cx^{2}}}.}$
It can be evaluated by completing the square in the denominator.
${\\displaystyle \\int {\ rac {dx}{a+bx+cx^{2}}}={\ rac {1}{c}}\\int {\ rac {dx}{\\left(x+{\ rac {b}{2c}}\ ight)^{\\!2}+\\left({\ rac {a}{c}}-{\ rac {b^{2}}{4c^{2}}}\ ight)}}.}$
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Quadratic_integral)

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