Optimal. Leaf size=47 \[ \frac {a^3 x^3}{3}+\frac {9}{10} a^2 b x^{10/3}+\frac {9}{11} a b^2 x^{11/3}+\frac {b^3 x^4}{4} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {272, 45}
\begin {gather*} \frac {a^3 x^3}{3}+\frac {9}{10} a^2 b x^{10/3}+\frac {9}{11} a b^2 x^{11/3}+\frac {b^3 x^4}{4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 45
Rule 272
Rubi steps
\begin {align*} \int \left (a+b \sqrt [3]{x}\right )^3 x^2 \, dx &=3 \text {Subst}\left (\int x^8 (a+b x)^3 \, dx,x,\sqrt [3]{x}\right )\\ &=3 \text {Subst}\left (\int \left (a^3 x^8+3 a^2 b x^9+3 a b^2 x^{10}+b^3 x^{11}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=\frac {a^3 x^3}{3}+\frac {9}{10} a^2 b x^{10/3}+\frac {9}{11} a b^2 x^{11/3}+\frac {b^3 x^4}{4}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 41, normalized size = 0.87 \begin {gather*} \frac {1}{660} x^3 \left (220 a^3+594 a^2 b \sqrt [3]{x}+540 a b^2 x^{2/3}+165 b^3 x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.18, size = 36, normalized size = 0.77
method | result | size |
derivativedivides | \(\frac {a^{3} x^{3}}{3}+\frac {9 a^{2} b \,x^{\frac {10}{3}}}{10}+\frac {9 a \,b^{2} x^{\frac {11}{3}}}{11}+\frac {b^{3} x^{4}}{4}\) | \(36\) |
default | \(\frac {a^{3} x^{3}}{3}+\frac {9 a^{2} b \,x^{\frac {10}{3}}}{10}+\frac {9 a \,b^{2} x^{\frac {11}{3}}}{11}+\frac {b^{3} x^{4}}{4}\) | \(36\) |
trager | \(\frac {\left (3 b^{3} x^{3}+4 a^{3} x^{2}+3 b^{3} x^{2}+4 a^{3} x +3 b^{3} x +4 a^{3}+3 b^{3}\right ) \left (x -1\right )}{12}+\frac {9 a^{2} b \,x^{\frac {10}{3}}}{10}+\frac {9 a \,b^{2} x^{\frac {11}{3}}}{11}\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 149 vs.
\(2 (35) = 70\).
time = 0.30, size = 149, normalized size = 3.17 \begin {gather*} \frac {{\left (b x^{\frac {1}{3}} + a\right )}^{12}}{4 \, b^{9}} - \frac {24 \, {\left (b x^{\frac {1}{3}} + a\right )}^{11} a}{11 \, b^{9}} + \frac {42 \, {\left (b x^{\frac {1}{3}} + a\right )}^{10} a^{2}}{5 \, b^{9}} - \frac {56 \, {\left (b x^{\frac {1}{3}} + a\right )}^{9} a^{3}}{3 \, b^{9}} + \frac {105 \, {\left (b x^{\frac {1}{3}} + a\right )}^{8} a^{4}}{4 \, b^{9}} - \frac {24 \, {\left (b x^{\frac {1}{3}} + a\right )}^{7} a^{5}}{b^{9}} + \frac {14 \, {\left (b x^{\frac {1}{3}} + a\right )}^{6} a^{6}}{b^{9}} - \frac {24 \, {\left (b x^{\frac {1}{3}} + a\right )}^{5} a^{7}}{5 \, b^{9}} + \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{4} a^{8}}{4 \, b^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 35, normalized size = 0.74 \begin {gather*} \frac {1}{4} \, b^{3} x^{4} + \frac {9}{11} \, a b^{2} x^{\frac {11}{3}} + \frac {9}{10} \, a^{2} b x^{\frac {10}{3}} + \frac {1}{3} \, a^{3} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.87, size = 42, normalized size = 0.89 \begin {gather*} \frac {a^{3} x^{3}}{3} + \frac {9 a^{2} b x^{\frac {10}{3}}}{10} + \frac {9 a b^{2} x^{\frac {11}{3}}}{11} + \frac {b^{3} x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.81, size = 35, normalized size = 0.74 \begin {gather*} \frac {1}{4} \, b^{3} x^{4} + \frac {9}{11} \, a b^{2} x^{\frac {11}{3}} + \frac {9}{10} \, a^{2} b x^{\frac {10}{3}} + \frac {1}{3} \, a^{3} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 35, normalized size = 0.74 \begin {gather*} \frac {a^3\,x^3}{3}+\frac {b^3\,x^4}{4}+\frac {9\,a^2\,b\,x^{10/3}}{10}+\frac {9\,a\,b^2\,x^{11/3}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________