Optimal. Leaf size=66 \[ \frac{36 b \sqrt [6]{a+b x}}{7 \sqrt [6]{c+d x} (b c-a d)^2}+\frac{6 \sqrt [6]{a+b x}}{7 (c+d x)^{7/6} (b c-a d)} \]
[Out]
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Rubi [A] time = 0.0517297, antiderivative size = 66, 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 \[ \frac{36 b \sqrt [6]{a+b x}}{7 \sqrt [6]{c+d x} (b c-a d)^2}+\frac{6 \sqrt [6]{a+b x}}{7 (c+d x)^{7/6} (b c-a d)} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x)^(5/6)*(c + d*x)^(13/6)),x]
[Out]
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Rubi in Sympy [A] time = 6.91437, size = 56, normalized size = 0.85 \[ \frac{36 b \sqrt [6]{a + b x}}{7 \sqrt [6]{c + d x} \left (a d - b c\right )^{2}} - \frac{6 \sqrt [6]{a + b x}}{7 \left (c + d x\right )^{\frac{7}{6}} \left (a d - b c\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)**(5/6)/(d*x+c)**(13/6),x)
[Out]
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Mathematica [A] time = 0.0600439, size = 46, normalized size = 0.7 \[ \frac{6 \sqrt [6]{a+b x} (-a d+7 b c+6 b d x)}{7 (c+d x)^{7/6} (b c-a d)^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x)^(5/6)*(c + d*x)^(13/6)),x]
[Out]
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Maple [A] time = 0.007, size = 53, normalized size = 0.8 \[ -{\frac{-36\,bdx+6\,ad-42\,bc}{7\,{a}^{2}{d}^{2}-14\,abcd+7\,{b}^{2}{c}^{2}}\sqrt [6]{bx+a} \left ( dx+c \right ) ^{-{\frac{7}{6}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)^(5/6)/(d*x+c)^(13/6),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{5}{6}}{\left (d x + c\right )}^{\frac{13}{6}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(5/6)*(d*x + c)^(13/6)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213918, size = 159, normalized size = 2.41 \[ \frac{6 \,{\left (6 \, b d x + 7 \, b c - a d\right )}{\left (b x + a\right )}^{\frac{1}{6}}{\left (d x + c\right )}^{\frac{5}{6}}}{7 \,{\left (b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} +{\left (b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right )} x^{2} + 2 \,{\left (b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right )} x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(5/6)*(d*x + c)^(13/6)),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(1/(b*x+a)**(5/6)/(d*x+c)**(13/6),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(1/((b*x + a)^(5/6)*(d*x + c)^(13/6)),x, algorithm="giac")
[Out]