Optimal. Leaf size=74 \[ \frac{6 (a+b x)^{13/6} \sqrt [6]{c+d x} \, _2F_1\left (-\frac{1}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right )}{13 b \sqrt [6]{\frac{b (c+d x)}{b c-a d}}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0846937, antiderivative size = 74, 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 \[ \frac{6 (a+b x)^{13/6} \sqrt [6]{c+d x} \, _2F_1\left (-\frac{1}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right )}{13 b \sqrt [6]{\frac{b (c+d x)}{b c-a d}}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^(7/6)*(c + d*x)^(1/6),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 13.7489, size = 70, normalized size = 0.95 \[ \frac{6 \sqrt [6]{a + b x} \left (c + d x\right )^{\frac{7}{6}} \left (a d - b c\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{7}{6}, \frac{7}{6} \\ \frac{13}{6} \end{matrix}\middle |{\frac{b \left (- c - d x\right )}{a d - b c}} \right )}}{7 d^{2} \sqrt [6]{\frac{d \left (a + b x\right )}{a d - b c}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**(7/6)*(d*x+c)**(1/6),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.265569, size = 142, normalized size = 1.92 \[ -\frac{3 \sqrt [6]{c+d x} \left (-d (a+b x) \left (7 a^2 d^2+2 a b d (8 c+15 d x)+b^2 \left (-7 c^2+2 c d x+16 d^2 x^2\right )\right )-7 (b c-a d)^3 \left (\frac{d (a+b x)}{a d-b c}\right )^{5/6} \, _2F_1\left (\frac{1}{6},\frac{5}{6};\frac{7}{6};\frac{b (c+d x)}{b c-a d}\right )\right )}{112 b d^3 (a+b x)^{5/6}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^(7/6)*(c + d*x)^(1/6),x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.05, size = 0, normalized size = 0. \[ \int \left ( bx+a \right ) ^{{\frac{7}{6}}}\sqrt [6]{dx+c}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^(7/6)*(d*x+c)^(1/6),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (b x + a\right )}^{\frac{7}{6}}{\left (d x + c\right )}^{\frac{1}{6}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(7/6)*(d*x + c)^(1/6),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left ({\left (b x + a\right )}^{\frac{7}{6}}{\left (d x + c\right )}^{\frac{1}{6}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(7/6)*(d*x + c)^(1/6),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((b*x+a)**(7/6)*(d*x+c)**(1/6),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [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)^(7/6)*(d*x + c)^(1/6),x, algorithm="giac")
[Out]