Optimal. Leaf size=78 \[ \frac{9 a^2 x}{14 c^3 \sqrt [3]{c+d x^3}}+\frac{3 a x \left (a+b x^3\right )}{14 c^2 \left (c+d x^3\right )^{4/3}}+\frac{x \left (a+b x^3\right )^2}{7 c \left (c+d x^3\right )^{7/3}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0701422, antiderivative size = 78, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ \frac{9 a^2 x}{14 c^3 \sqrt [3]{c+d x^3}}+\frac{3 a x \left (a+b x^3\right )}{14 c^2 \left (c+d x^3\right )^{4/3}}+\frac{x \left (a+b x^3\right )^2}{7 c \left (c+d x^3\right )^{7/3}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^2/(c + d*x^3)^(10/3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 11.2865, size = 71, normalized size = 0.91 \[ \frac{9 a^{2} x}{14 c^{3} \sqrt [3]{c + d x^{3}}} + \frac{3 a x \left (a + b x^{3}\right )}{14 c^{2} \left (c + d x^{3}\right )^{\frac{4}{3}}} + \frac{x \left (a + b x^{3}\right )^{2}}{7 c \left (c + d x^{3}\right )^{\frac{7}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**2/(d*x**3+c)**(10/3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0835213, size = 73, normalized size = 0.94 \[ \frac{a^2 \left (14 c^2 x+21 c d x^4+9 d^2 x^7\right )+a b c x^4 \left (7 c+3 d x^3\right )+2 b^2 c^2 x^7}{14 c^3 \left (c+d x^3\right )^{7/3}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^2/(c + d*x^3)^(10/3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 76, normalized size = 1. \[{\frac{x \left ( 9\,{a}^{2}{d}^{2}{x}^{6}+3\,abcd{x}^{6}+2\,{b}^{2}{c}^{2}{x}^{6}+21\,{a}^{2}cd{x}^{3}+7\,ab{c}^{2}{x}^{3}+14\,{a}^{2}{c}^{2} \right ) }{14\,{c}^{3}} \left ( d{x}^{3}+c \right ) ^{-{\frac{7}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^2/(d*x^3+c)^(10/3),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.38355, size = 147, normalized size = 1.88 \[ \frac{b^{2} x^{7}}{7 \,{\left (d x^{3} + c\right )}^{\frac{7}{3}} c} - \frac{a b{\left (4 \, d - \frac{7 \,{\left (d x^{3} + c\right )}}{x^{3}}\right )} x^{7}}{14 \,{\left (d x^{3} + c\right )}^{\frac{7}{3}} c^{2}} + \frac{{\left (2 \, d^{2} - \frac{7 \,{\left (d x^{3} + c\right )} d}{x^{3}} + \frac{14 \,{\left (d x^{3} + c\right )}^{2}}{x^{6}}\right )} a^{2} x^{7}}{14 \,{\left (d x^{3} + c\right )}^{\frac{7}{3}} c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/(d*x^3 + c)^(10/3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.21906, size = 139, normalized size = 1.78 \[ \frac{{\left ({\left (2 \, b^{2} c^{2} + 3 \, a b c d + 9 \, a^{2} d^{2}\right )} x^{7} + 14 \, a^{2} c^{2} x + 7 \,{\left (a b c^{2} + 3 \, a^{2} c d\right )} x^{4}\right )}{\left (d x^{3} + c\right )}^{\frac{2}{3}}}{14 \,{\left (c^{3} d^{3} x^{9} + 3 \, c^{4} d^{2} x^{6} + 3 \, c^{5} d x^{3} + c^{6}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/(d*x^3 + c)^(10/3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
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((b*x**3+a)**2/(d*x**3+c)**(10/3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{3} + a\right )}^{2}}{{\left (d x^{3} + c\right )}^{\frac{10}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2/(d*x^3 + c)^(10/3),x, algorithm="giac")
[Out]