Optimal. Leaf size=32 \[ \frac{3 (c+d x)^{2/3}}{2 d^2 \sqrt [3]{a d+b c+2 b d x}} \]
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Rubi [A] time = 0.0431683, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 31, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.032 \[ \frac{3 (c+d x)^{2/3}}{2 d^2 \sqrt [3]{a d+b c+2 b d x}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]
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Rubi in Sympy [A] time = 7.89092, size = 31, normalized size = 0.97 \[ \frac{3 \left (c + d x\right )^{\frac{2}{3}}}{2 d^{2} \sqrt [3]{a d + b c + 2 b d x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/(d*x+c)**(1/3)/(2*b*d*x+a*d+b*c)**(4/3),x)
[Out]
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Mathematica [A] time = 0.096631, size = 32, normalized size = 1. \[ \frac{3 (c+d x)^{2/3}}{2 d^2 \sqrt [3]{a d+b (c+2 d x)}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/((c + d*x)^(1/3)*(b*c + a*d + 2*b*d*x)^(4/3)),x]
[Out]
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Maple [A] time = 0.009, size = 27, normalized size = 0.8 \[{\frac{3}{2\,{d}^{2}} \left ( dx+c \right ) ^{{\frac{2}{3}}}{\frac{1}{\sqrt [3]{2\,bdx+ad+bc}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(4/3),x)
[Out]
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Maxima [A] time = 1.52187, size = 35, normalized size = 1.09 \[ \frac{3 \,{\left (d x + c\right )}^{\frac{2}{3}}}{2 \,{\left (2 \, b d x + b c + a d\right )}^{\frac{1}{3}} d^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/((2*b*d*x + b*c + a*d)^(4/3)*(d*x + c)^(1/3)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.321613, size = 59, normalized size = 1.84 \[ \frac{3 \,{\left (2 \, b d x + b c + a d\right )}^{\frac{2}{3}}{\left (d x + c\right )}^{\frac{2}{3}}}{2 \,{\left (2 \, b d^{3} x + b c d^{2} + a d^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/((2*b*d*x + b*c + a*d)^(4/3)*(d*x + c)^(1/3)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{a + b x}{\sqrt [3]{c + d x} \left (a d + b c + 2 b d x\right )^{\frac{4}{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/(d*x+c)**(1/3)/(2*b*d*x+a*d+b*c)**(4/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{b x + a}{{\left (2 \, b d x + b c + a d\right )}^{\frac{4}{3}}{\left (d x + c\right )}^{\frac{1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/((2*b*d*x + b*c + a*d)^(4/3)*(d*x + c)^(1/3)),x, algorithm="giac")
[Out]