Optimal. Leaf size=74 \[ \frac{6 (a+b x)^{13/6} \left (\frac{b (c+d x)}{b c-a d}\right )^{5/6} \, _2F_1\left (\frac{5}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right )}{13 b (c+d x)^{5/6}} \]
[Out]
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Rubi [A] time = 0.0853894, 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 \[ \frac{6 (a+b x)^{13/6} \left (\frac{b (c+d x)}{b c-a d}\right )^{5/6} \, _2F_1\left (\frac{5}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right )}{13 b (c+d x)^{5/6}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^(7/6)/(c + d*x)^(5/6),x]
[Out]
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Rubi in Sympy [A] time = 13.3608, size = 68, normalized size = 0.92 \[ \frac{6 \sqrt [6]{a + b x} \sqrt [6]{c + d x} \left (a d - b c\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{7}{6}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle |{\frac{b \left (- c - d x\right )}{a d - b c}} \right )}}{d^{2} \sqrt [6]{\frac{d \left (a + b x\right )}{a d - b c}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**(7/6)/(d*x+c)**(5/6),x)
[Out]
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Mathematica [A] time = 0.188247, size = 107, normalized size = 1.45 \[ \frac{3 \sqrt [6]{c+d x} \left (7 (b c-a d)^2 \left (\frac{d (a+b x)}{a d-b c}\right )^{5/6} \, _2F_1\left (\frac{1}{6},\frac{5}{6};\frac{7}{6};\frac{b (c+d x)}{b c-a d}\right )+d (a+b x) (9 a d-7 b c+2 b d x)\right )}{8 d^3 (a+b x)^{5/6}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^(7/6)/(c + d*x)^(5/6),x]
[Out]
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Maple [F] time = 0.051, size = 0, normalized size = 0. \[ \int{1 \left ( bx+a \right ) ^{{\frac{7}{6}}} \left ( dx+c \right ) ^{-{\frac{5}{6}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^(7/6)/(d*x+c)^(5/6),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x + a\right )}^{\frac{7}{6}}}{{\left (d x + c\right )}^{\frac{5}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(7/6)/(d*x + c)^(5/6),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (b x + a\right )}^{\frac{7}{6}}}{{\left (d x + c\right )}^{\frac{5}{6}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(7/6)/(d*x + c)^(5/6),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((b*x+a)**(7/6)/(d*x+c)**(5/6),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((b*x + a)^(7/6)/(d*x + c)^(5/6),x, algorithm="giac")
[Out]