Optimal. Leaf size=80 \[ -\frac{6 b \sqrt [6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left (-\frac{1}{6},\frac{13}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right )}{\sqrt [6]{a+b x} \sqrt [6]{c+d x} (b c-a d)^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0904365, antiderivative size = 80, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ -\frac{6 b \sqrt [6]{\frac{b (c+d x)}{b c-a d}} \, _2F_1\left (-\frac{1}{6},\frac{13}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right )}{\sqrt [6]{a+b x} \sqrt [6]{c+d x} (b c-a d)^2} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x)^(7/6)*(c + d*x)^(13/6)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 14.2498, size = 73, normalized size = 0.91 \[ - \frac{6 d \left (a + b x\right )^{\frac{5}{6}}{{}_{2}F_{1}\left (\begin{matrix} \frac{7}{6}, - \frac{7}{6} \\ - \frac{1}{6} \end{matrix}\middle |{\frac{b \left (- c - d x\right )}{a d - b c}} \right )}}{7 \left (\frac{d \left (a + b x\right )}{a d - b c}\right )^{\frac{5}{6}} \left (c + d x\right )^{\frac{7}{6}} \left (a d - b c\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)**(7/6)/(d*x+c)**(13/6),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.404952, size = 138, normalized size = 1.72 \[ \frac{6 \left (5 a^2 d^2+64 b^2 (c+d x)^2 \sqrt [6]{\frac{d (a+b x)}{a d-b c}} \, _2F_1\left (\frac{1}{6},\frac{5}{6};\frac{11}{6};\frac{b (c+d x)}{b c-a d}\right )-10 a b d (5 c+4 d x)-5 b^2 \left (7 c^2+24 c d x+16 d^2 x^2\right )\right )}{35 \sqrt [6]{a+b x} (c+d x)^{7/6} (b c-a d)^3} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x)^(7/6)*(c + d*x)^(13/6)),x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.056, size = 0, normalized size = 0. \[ \int{1 \left ( bx+a \right ) ^{-{\frac{7}{6}}} \left ( dx+c \right ) ^{-{\frac{13}{6}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)^(7/6)/(d*x+c)^(13/6),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{7}{6}}{\left (d x + c\right )}^{\frac{13}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(7/6)*(d*x + c)^(13/6)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{{\left (b d^{2} x^{3} + a c^{2} +{\left (2 \, b c d + a d^{2}\right )} x^{2} +{\left (b c^{2} + 2 \, a c d\right )} x\right )}{\left (b x + a\right )}^{\frac{1}{6}}{\left (d x + c\right )}^{\frac{1}{6}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(7/6)*(d*x + c)^(13/6)),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(1/(b*x+a)**(7/6)/(d*x+c)**(13/6),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{7}{6}}{\left (d x + c\right )}^{\frac{13}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(7/6)*(d*x + c)^(13/6)),x, algorithm="giac")
[Out]