Optimal. Leaf size=32 \[ \frac{3 (a+b x)^{4/3}}{4 b^2}-\frac{3 a \sqrt [3]{a+b x}}{b^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0252886, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{3 (a+b x)^{4/3}}{4 b^2}-\frac{3 a \sqrt [3]{a+b x}}{b^2} \]
Antiderivative was successfully verified.
[In] Int[x/(a + b*x)^(2/3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.93823, size = 29, normalized size = 0.91 \[ - \frac{3 a \sqrt [3]{a + b x}}{b^{2}} + \frac{3 \left (a + b x\right )^{\frac{4}{3}}}{4 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b*x+a)**(2/3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0133343, size = 23, normalized size = 0.72 \[ \frac{3 (b x-3 a) \sqrt [3]{a+b x}}{4 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a + b*x)^(2/3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 21, normalized size = 0.7 \[ -{\frac{-3\,bx+9\,a}{4\,{b}^{2}}\sqrt [3]{bx+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b*x+a)^(2/3),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33157, size = 35, normalized size = 1.09 \[ \frac{3 \,{\left (b x + a\right )}^{\frac{4}{3}}}{4 \, b^{2}} - \frac{3 \,{\left (b x + a\right )}^{\frac{1}{3}} a}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x + a)^(2/3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.209765, size = 26, normalized size = 0.81 \[ \frac{3 \,{\left (b x + a\right )}^{\frac{1}{3}}{\left (b x - 3 \, a\right )}}{4 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x + a)^(2/3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 3.6257, size = 162, normalized size = 5.06 \[ - \frac{9 a^{\frac{10}{3}} \sqrt [3]{1 + \frac{b x}{a}}}{4 a^{2} b^{2} + 4 a b^{3} x} + \frac{9 a^{\frac{10}{3}}}{4 a^{2} b^{2} + 4 a b^{3} x} - \frac{6 a^{\frac{7}{3}} b x \sqrt [3]{1 + \frac{b x}{a}}}{4 a^{2} b^{2} + 4 a b^{3} x} + \frac{9 a^{\frac{7}{3}} b x}{4 a^{2} b^{2} + 4 a b^{3} x} + \frac{3 a^{\frac{4}{3}} b^{2} x^{2} \sqrt [3]{1 + \frac{b x}{a}}}{4 a^{2} b^{2} + 4 a b^{3} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x+a)**(2/3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.202691, size = 31, normalized size = 0.97 \[ \frac{3 \,{\left ({\left (b x + a\right )}^{\frac{4}{3}} - 4 \,{\left (b x + a\right )}^{\frac{1}{3}} a\right )}}{4 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x + a)^(2/3),x, algorithm="giac")
[Out]