Optimal. Leaf size=72 \[ -\frac{6 (c+d x)^{5/6} \, _2F_1\left (-\frac{5}{6},-\frac{1}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right )}{b \sqrt [6]{a+b x} \left (\frac{b (c+d x)}{b c-a d}\right )^{5/6}} \]
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Rubi [A] time = 0.0874622, antiderivative size = 72, 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 \[ -\frac{6 (c+d x)^{5/6} \, _2F_1\left (-\frac{5}{6},-\frac{1}{6};\frac{5}{6};-\frac{d (a+b x)}{b c-a d}\right )}{b \sqrt [6]{a+b x} \left (\frac{b (c+d x)}{b c-a d}\right )^{5/6}} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x)^(5/6)/(a + b*x)^(7/6),x]
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Rubi in Sympy [A] time = 14.1892, size = 68, normalized size = 0.94 \[ \frac{6 d \left (a + b x\right )^{\frac{5}{6}} \left (c + d x\right )^{\frac{11}{6}}{{}_{2}F_{1}\left (\begin{matrix} \frac{7}{6}, \frac{11}{6} \\ \frac{17}{6} \end{matrix}\middle |{\frac{b \left (- c - d x\right )}{a d - b c}} \right )}}{11 \left (\frac{d \left (a + b x\right )}{a d - b c}\right )^{\frac{5}{6}} \left (a d - b c\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((d*x+c)**(5/6)/(b*x+a)**(7/6),x)
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Mathematica [A] time = 0.106784, size = 74, normalized size = 1.03 \[ \frac{6 (c+d x)^{5/6} \left (\sqrt [6]{\frac{d (a+b x)}{a d-b c}} \, _2F_1\left (\frac{1}{6},\frac{5}{6};\frac{11}{6};\frac{b (c+d x)}{b c-a d}\right )-1\right )}{b \sqrt [6]{a+b x}} \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x)^(5/6)/(a + b*x)^(7/6),x]
[Out]
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Maple [F] time = 0.043, size = 0, normalized size = 0. \[ \int{1 \left ( dx+c \right ) ^{{\frac{5}{6}}} \left ( bx+a \right ) ^{-{\frac{7}{6}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((d*x+c)^(5/6)/(b*x+a)^(7/6),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (d x + c\right )}^{\frac{5}{6}}}{{\left (b x + a\right )}^{\frac{7}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(5/6)/(b*x + a)^(7/6),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (d x + c\right )}^{\frac{5}{6}}}{{\left (b x + a\right )}^{\frac{7}{6}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^(5/6)/(b*x + a)^(7/6),x, algorithm="fricas")
[Out]
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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((d*x+c)**(5/6)/(b*x+a)**(7/6),x)
[Out]
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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((d*x + c)^(5/6)/(b*x + a)^(7/6),x, algorithm="giac")
[Out]