Optimal. Leaf size=30 \[ -\frac{3 \sqrt [3]{c+d x}}{\sqrt [3]{a+b x} (b c-a d)} \]
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Rubi [A] time = 0.0252009, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ -\frac{3 \sqrt [3]{c+d x}}{\sqrt [3]{a+b x} (b c-a d)} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x)^(4/3)*(c + d*x)^(2/3)),x]
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Rubi in Sympy [A] time = 3.27639, size = 24, normalized size = 0.8 \[ \frac{3 \sqrt [3]{c + d x}}{\sqrt [3]{a + b x} \left (a d - b c\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)**(4/3)/(d*x+c)**(2/3),x)
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Mathematica [A] time = 0.0327291, size = 30, normalized size = 1. \[ \frac{3 \sqrt [3]{c+d x}}{\sqrt [3]{a+b x} (a d-b c)} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x)^(4/3)*(c + d*x)^(2/3)),x]
[Out]
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Maple [A] time = 0.007, size = 27, normalized size = 0.9 \[ 3\,{\frac{\sqrt [3]{dx+c}}{\sqrt [3]{bx+a} \left ( ad-bc \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)^(4/3)/(d*x+c)^(2/3),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{4}{3}}{\left (d x + c\right )}^{\frac{2}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(4/3)*(d*x + c)^(2/3)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204533, size = 57, normalized size = 1.9 \[ -\frac{3 \,{\left (b x + a\right )}^{\frac{2}{3}}{\left (d x + c\right )}^{\frac{1}{3}}}{a b c - a^{2} d +{\left (b^{2} c - a b d\right )} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(4/3)*(d*x + c)^(2/3)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (a + b x\right )^{\frac{4}{3}} \left (c + d x\right )^{\frac{2}{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x+a)**(4/3)/(d*x+c)**(2/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{4}{3}}{\left (d x + c\right )}^{\frac{2}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(4/3)*(d*x + c)^(2/3)),x, algorithm="giac")
[Out]