Optimal. Leaf size=47 \[ \frac{\sqrt{\pi } \text{Erf}\left (\sqrt{c} \sqrt{\log (F)} (a+b x)^{n/2}\right )}{b \sqrt{c} n \sqrt{\log (F)}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0796287, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{\sqrt{\pi } \text{Erf}\left (\sqrt{c} \sqrt{\log (F)} (a+b x)^{n/2}\right )}{b \sqrt{c} n \sqrt{\log (F)}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^(-1 + n/2)/F^(c*(a + b*x)^n),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 7.67416, size = 41, normalized size = 0.87 \[ \frac{\sqrt{\pi } \operatorname{erf}{\left (\sqrt{c} \left (a + b x\right )^{\frac{n}{2}} \sqrt{\log{\left (F \right )}} \right )}}{b \sqrt{c} n \sqrt{\log{\left (F \right )}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**(-1+1/2*n)/(F**(c*(b*x+a)**n)),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.054392, size = 0, normalized size = 0. \[ \int F^{-c (a+b x)^n} (a+b x)^{-1+\frac{n}{2}} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[(a + b*x)^(-1 + n/2)/F^(c*(a + b*x)^n),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.099, size = 34, normalized size = 0.7 \[{\frac{\sqrt{\pi }}{bn}{\it Erf} \left ( \sqrt{c\ln \left ( F \right ) } \left ( bx+a \right ) ^{{\frac{n}{2}}} \right ){\frac{1}{\sqrt{c\ln \left ( F \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^(-1+1/2*n)/(F^(c*(b*x+a)^n)),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x + a\right )}^{\frac{1}{2} \, n - 1}}{F^{{\left (b x + a\right )}^{n} c}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(1/2*n - 1)/F^((b*x + a)^n*c),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.275886, size = 54, normalized size = 1.15 \[ \frac{\sqrt{\pi } \operatorname{erf}\left ({\left (b x + a\right )} \sqrt{c \log \left (F\right )}{\left (b x + a\right )}^{\frac{1}{2} \, n - 1}\right )}{\sqrt{c \log \left (F\right )} b n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(1/2*n - 1)/F^((b*x + a)^n*c),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**(-1+1/2*n)/(F**(c*(b*x+a)**n)),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x + a\right )}^{\frac{1}{2} \, n - 1}}{F^{{\left (b x + a\right )}^{n} c}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(1/2*n - 1)/F^((b*x + a)^n*c),x, algorithm="giac")
[Out]