Optimal. Leaf size=101 \[ -\frac{27 d^2 (c+d x)^{2/3}}{40 (a+b x)^{2/3} (b c-a d)^3}+\frac{9 d (c+d x)^{2/3}}{20 (a+b x)^{5/3} (b c-a d)^2}-\frac{3 (c+d x)^{2/3}}{8 (a+b x)^{8/3} (b c-a d)} \]
[Out]
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Rubi [A] time = 0.0872245, antiderivative size = 101, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ -\frac{27 d^2 (c+d x)^{2/3}}{40 (a+b x)^{2/3} (b c-a d)^3}+\frac{9 d (c+d x)^{2/3}}{20 (a+b x)^{5/3} (b c-a d)^2}-\frac{3 (c+d x)^{2/3}}{8 (a+b x)^{8/3} (b c-a d)} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x)^(11/3)*(c + d*x)^(1/3)),x]
[Out]
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Rubi in Sympy [A] time = 13.5638, size = 88, normalized size = 0.87 \[ \frac{27 d^{2} \left (c + d x\right )^{\frac{2}{3}}}{40 \left (a + b x\right )^{\frac{2}{3}} \left (a d - b c\right )^{3}} + \frac{9 d \left (c + d x\right )^{\frac{2}{3}}}{20 \left (a + b x\right )^{\frac{5}{3}} \left (a d - b c\right )^{2}} + \frac{3 \left (c + d x\right )^{\frac{2}{3}}}{8 \left (a + b x\right )^{\frac{8}{3}} \left (a d - b c\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)**(11/3)/(d*x+c)**(1/3),x)
[Out]
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Mathematica [A] time = 0.0969337, size = 77, normalized size = 0.76 \[ -\frac{3 (c+d x)^{2/3} \left (20 a^2 d^2+8 a b d (3 d x-2 c)+b^2 \left (5 c^2-6 c d x+9 d^2 x^2\right )\right )}{40 (a+b x)^{8/3} (b c-a d)^3} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x)^(11/3)*(c + d*x)^(1/3)),x]
[Out]
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Maple [A] time = 0.01, size = 105, normalized size = 1. \[{\frac{27\,{b}^{2}{d}^{2}{x}^{2}+72\,ab{d}^{2}x-18\,{b}^{2}cdx+60\,{a}^{2}{d}^{2}-48\,abcd+15\,{b}^{2}{c}^{2}}{40\,{a}^{3}{d}^{3}-120\,{a}^{2}cb{d}^{2}+120\,a{b}^{2}{c}^{2}d-40\,{b}^{3}{c}^{3}} \left ( dx+c \right ) ^{{\frac{2}{3}}} \left ( bx+a \right ) ^{-{\frac{8}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)^(11/3)/(d*x+c)^(1/3),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{11}{3}}{\left (d x + c\right )}^{\frac{1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(11/3)*(d*x + c)^(1/3)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212706, size = 317, normalized size = 3.14 \[ -\frac{3 \,{\left (9 \, b^{2} d^{3} x^{3} + 5 \, b^{2} c^{3} - 16 \, a b c^{2} d + 20 \, a^{2} c d^{2} + 3 \,{\left (b^{2} c d^{2} + 8 \, a b d^{3}\right )} x^{2} -{\left (b^{2} c^{2} d - 8 \, a b c d^{2} - 20 \, a^{2} d^{3}\right )} x\right )}}{40 \,{\left (a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3} +{\left (b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right )} x^{2} + 2 \,{\left (a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right )} x\right )}{\left (b x + a\right )}^{\frac{2}{3}}{\left (d x + c\right )}^{\frac{1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(11/3)*(d*x + c)^(1/3)),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)**(11/3)/(d*x+c)**(1/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{11}{3}}{\left (d x + c\right )}^{\frac{1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(11/3)*(d*x + c)^(1/3)),x, algorithm="giac")
[Out]