Optimal. Leaf size=82 \[ \frac{6 (a+b x)^{13/6} \sqrt [6]{c+d x} (b c-a d) \, _2F_1\left (-\frac{7}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right )}{13 b^2 \sqrt [6]{\frac{b (c+d x)}{b c-a d}}} \]
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Rubi [A] time = 0.096567, antiderivative size = 82, 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 \[ \frac{6 (a+b x)^{13/6} \sqrt [6]{c+d x} (b c-a d) \, _2F_1\left (-\frac{7}{6},\frac{13}{6};\frac{19}{6};-\frac{d (a+b x)}{b c-a d}\right )}{13 b^2 \sqrt [6]{\frac{b (c+d x)}{b c-a d}}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^(7/6)*(c + d*x)^(7/6),x]
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Rubi in Sympy [A] time = 15.7937, size = 70, normalized size = 0.85 \[ \frac{6 \sqrt [6]{a + b x} \left (c + d x\right )^{\frac{13}{6}} \left (a d - b c\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{7}{6}, \frac{13}{6} \\ \frac{19}{6} \end{matrix}\middle |{\frac{b \left (- c - d x\right )}{a d - b c}} \right )}}{13 d^{2} \sqrt [6]{\frac{d \left (a + b x\right )}{a d - b c}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**(7/6)*(d*x+c)**(7/6),x)
[Out]
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Mathematica [B] time = 0.346107, size = 183, normalized size = 2.23 \[ \frac{3 \sqrt [6]{c+d x} \left (7 (b c-a d)^4 \left (\frac{d (a+b x)}{a d-b c}\right )^{5/6} \, _2F_1\left (\frac{1}{6},\frac{5}{6};\frac{7}{6};\frac{b (c+d x)}{b c-a d}\right )-d (a+b x) \left (7 a^3 d^3-a^2 b d^2 (23 c+2 d x)-a b^2 d \left (23 c^2+92 c d x+48 d^2 x^2\right )+b^3 \left (7 c^3-2 c^2 d x-48 c d^2 x^2-32 d^3 x^3\right )\right )\right )}{320 b^2 d^3 (a+b x)^{5/6}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^(7/6)*(c + d*x)^(7/6),x]
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Maple [F] time = 0.052, size = 0, normalized size = 0. \[ \int \left ( bx+a \right ) ^{{\frac{7}{6}}} \left ( dx+c \right ) ^{{\frac{7}{6}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^(7/6)*(d*x+c)^(7/6),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (b x + a\right )}^{\frac{7}{6}}{\left (d x + c\right )}^{\frac{7}{6}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(7/6)*(d*x + c)^(7/6),x, algorithm="maxima")
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left ({\left (b d x^{2} + a c +{\left (b c + a d\right )} x\right )}{\left (b x + a\right )}^{\frac{1}{6}}{\left (d x + c\right )}^{\frac{1}{6}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^(7/6)*(d*x + c)^(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((b*x+a)**(7/6)*(d*x+c)**(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((b*x + a)^(7/6)*(d*x + c)^(7/6),x, algorithm="giac")
[Out]