Optimal. Leaf size=59 \[ \frac{a^2 \left (a+b \sqrt [3]{x}\right )^6}{2 b^3}+\frac{3 \left (a+b \sqrt [3]{x}\right )^8}{8 b^3}-\frac{6 a \left (a+b \sqrt [3]{x}\right )^7}{7 b^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.080046, antiderivative size = 59, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{a^2 \left (a+b \sqrt [3]{x}\right )^6}{2 b^3}+\frac{3 \left (a+b \sqrt [3]{x}\right )^8}{8 b^3}-\frac{6 a \left (a+b \sqrt [3]{x}\right )^7}{7 b^3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 12.1733, size = 53, normalized size = 0.9 \[ \frac{a^{2} \left (a + b \sqrt [3]{x}\right )^{6}}{2 b^{3}} - \frac{6 a \left (a + b \sqrt [3]{x}\right )^{7}}{7 b^{3}} + \frac{3 \left (a + b \sqrt [3]{x}\right )^{8}}{8 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0126144, size = 68, normalized size = 1.15 \[ a^5 x+\frac{15}{4} a^4 b x^{4/3}+6 a^3 b^2 x^{5/3}+5 a^2 b^3 x^2+\frac{15}{7} a b^4 x^{7/3}+\frac{3}{8} b^5 x^{8/3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 55, normalized size = 0.9 \[ x{a}^{5}+{\frac{3\,{b}^{5}}{8}{x}^{{\frac{8}{3}}}}+{\frac{15\,a{b}^{4}}{7}{x}^{{\frac{7}{3}}}}+5\,{a}^{2}{b}^{3}{x}^{2}+6\,{a}^{3}{b}^{2}{x}^{5/3}+{\frac{15\,{a}^{4}b}{4}{x}^{{\frac{4}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43557, size = 73, normalized size = 1.24 \[ \frac{3}{8} \, b^{5} x^{\frac{8}{3}} + \frac{15}{7} \, a b^{4} x^{\frac{7}{3}} + 5 \, a^{2} b^{3} x^{2} + 6 \, a^{3} b^{2} x^{\frac{5}{3}} + \frac{15}{4} \, a^{4} b x^{\frac{4}{3}} + a^{5} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^5,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.208988, size = 82, normalized size = 1.39 \[ 5 \, a^{2} b^{3} x^{2} + a^{5} x + \frac{3}{8} \,{\left (b^{5} x^{2} + 16 \, a^{3} b^{2} x\right )} x^{\frac{2}{3}} + \frac{15}{28} \,{\left (4 \, a b^{4} x^{2} + 7 \, a^{4} b x\right )} x^{\frac{1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^5,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.42529, size = 68, normalized size = 1.15 \[ a^{5} x + \frac{15 a^{4} b x^{\frac{4}{3}}}{4} + 6 a^{3} b^{2} x^{\frac{5}{3}} + 5 a^{2} b^{3} x^{2} + \frac{15 a b^{4} x^{\frac{7}{3}}}{7} + \frac{3 b^{5} x^{\frac{8}{3}}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.229454, size = 73, normalized size = 1.24 \[ \frac{3}{8} \, b^{5} x^{\frac{8}{3}} + \frac{15}{7} \, a b^{4} x^{\frac{7}{3}} + 5 \, a^{2} b^{3} x^{2} + 6 \, a^{3} b^{2} x^{\frac{5}{3}} + \frac{15}{4} \, a^{4} b x^{\frac{4}{3}} + a^{5} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^5,x, algorithm="giac")
[Out]