Optimal. Leaf size=20 \[ -\frac {F^{\frac {1}{a+b x+c x^2}}}{\log (F)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.17, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {6706} \[ -\frac {F^{\frac {1}{a+b x+c x^2}}}{\log (F)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 6706
Rubi steps
\begin {align*} \int \frac {F^{\frac {1}{a+b x+c x^2}} (b+2 c x)}{\left (a+b x+c x^2\right )^2} \, dx &=-\frac {F^{\frac {1}{a+b x+c x^2}}}{\log (F)}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.42, size = 19, normalized size = 0.95 \[ -\frac {F^{\frac {1}{a+x (b+c x)}}}{\log (F)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.41, size = 20, normalized size = 1.00 \[ -\frac {F^{\left (\frac {1}{c x^{2} + b x + a}\right )}}{\log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.22, size = 20, normalized size = 1.00 \[ -\frac {F^{\left (\frac {1}{c x^{2} + b x + a}\right )}}{\log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 21, normalized size = 1.05 \[ -\frac {F^{\frac {1}{c \,x^{2}+b x +a}}}{\ln \relax (F )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.95, size = 20, normalized size = 1.00 \[ -\frac {F^{\left (\frac {1}{c x^{2} + b x + a}\right )}}{\log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.00, size = 20, normalized size = 1.00 \[ -\frac {F^{\frac {1}{c\,x^2+b\,x+a}}}{\ln \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.57, size = 32, normalized size = 1.60 \[ \begin {cases} - \frac {F^{\frac {1}{a + b x + c x^{2}}}}{\log {\relax (F )}} & \text {for}\: \log {\relax (F )} \neq 0 \\- \frac {1}{a + b x + c x^{2}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________