Optimal. Leaf size=16 \[ -\frac {2}{\sqrt {a+b x+c x^2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {629} \[ -\frac {2}{\sqrt {a+b x+c x^2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 629
Rubi steps
\begin {align*} \int \frac {b+2 c x}{\left (a+b x+c x^2\right )^{3/2}} \, dx &=-\frac {2}{\sqrt {a+b x+c x^2}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 15, normalized size = 0.94 \[ -\frac {2}{\sqrt {a+x (b+c x)}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.64, size = 14, normalized size = 0.88 \[ -\frac {2}{\sqrt {c x^{2} + b x + a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.21, size = 14, normalized size = 0.88 \[ -\frac {2}{\sqrt {c x^{2} + b x + a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 15, normalized size = 0.94 \[ -\frac {2}{\sqrt {c \,x^{2}+b x +a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.51, size = 14, normalized size = 0.88 \[ -\frac {2}{\sqrt {c x^{2} + b x + a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.89, size = 14, normalized size = 0.88 \[ -\frac {2}{\sqrt {c\,x^2+b\,x+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.92, size = 15, normalized size = 0.94 \[ - \frac {2}{\sqrt {a + b x + c x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________