Optimal. Leaf size=30 \[ \frac{3 \sqrt [3]{a+b x}}{\sqrt [3]{c+d x} (b c-a d)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.021083, 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 \[ \frac{3 \sqrt [3]{a+b x}}{\sqrt [3]{c+d x} (b c-a d)} \]
Antiderivative was successfully verified.
[In] Int[1/((a + b*x)^(2/3)*(c + d*x)^(4/3)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.60265, size = 26, normalized size = 0.87 \[ - \frac{3 \sqrt [3]{a + b x}}{\sqrt [3]{c + d x} \left (a d - b c\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+a)**(2/3)/(d*x+c)**(4/3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0370064, size = 30, normalized size = 1. \[ -\frac{3 \sqrt [3]{a+b x}}{\sqrt [3]{c+d x} (a d-b c)} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + b*x)^(2/3)*(c + d*x)^(4/3)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 27, normalized size = 0.9 \[ -3\,{\frac{\sqrt [3]{bx+a}}{\sqrt [3]{dx+c} \left ( ad-bc \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+a)^(2/3)/(d*x+c)^(4/3),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{2}{3}}{\left (d x + c\right )}^{\frac{4}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(2/3)*(d*x + c)^(4/3)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.222576, size = 57, normalized size = 1.9 \[ \frac{3 \,{\left (b x + a\right )}^{\frac{1}{3}}{\left (d x + c\right )}^{\frac{2}{3}}}{b c^{2} - a c d +{\left (b c d - a d^{2}\right )} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(2/3)*(d*x + c)^(4/3)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (a + b x\right )^{\frac{2}{3}} \left (c + d x\right )^{\frac{4}{3}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x+a)**(2/3)/(d*x+c)**(4/3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x + a\right )}^{\frac{2}{3}}{\left (d x + c\right )}^{\frac{4}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + a)^(2/3)*(d*x + c)^(4/3)),x, algorithm="giac")
[Out]