Optimal. Leaf size=56 \[ 2 \sqrt {x}+\frac {3 x^{2/3}}{2}+\frac {6 x^{5/6}}{5}+3 x+\frac {6 x^{7/6}}{7}+\frac {3 x^{4/3}}{4}+\frac {2 x^{3/2}}{3} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.06, antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {6874}
\begin {gather*} \frac {2 x^{3/2}}{3}+\frac {3 x^{4/3}}{4}+\frac {6 x^{7/6}}{7}+\frac {6 x^{5/6}}{5}+\frac {3 x^{2/3}}{2}+3 x+2 \sqrt {x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=6 \text {Subst}\left (\int x^2 \left (1+x+x^3\right ) \left (1+x^2+x^3\right ) \, dx,x,\sqrt [6]{x}\right )\\ &=6 \text {Subst}\left (\int \left (x^2+x^3+x^4+3 x^5+x^6+x^7+x^8\right ) \, dx,x,\sqrt [6]{x}\right )\\ &=2 \sqrt {x}+\frac {3 x^{2/3}}{2}+\frac {6 x^{5/6}}{5}+3 x+\frac {6 x^{7/6}}{7}+\frac {3 x^{4/3}}{4}+\frac {2 x^{3/2}}{3}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 50, normalized size = 0.89 \begin {gather*} \frac {1}{420} \left (840 \sqrt {x}+630 x^{2/3}+504 x^{5/6}+1260 x+360 x^{7/6}+315 x^{4/3}+280 x^{3/2}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 35, normalized size = 0.62 \[2 \sqrt {x}+\frac {3 x^{\frac {2}{3}}}{2}+\frac {6 x^{\frac {5}{6}}}{5}+3 x +\frac {6 x^{\frac {7}{6}}}{7}+\frac {3 x^{\frac {4}{3}}}{4}+\frac {2 x^{\frac {3}{2}}}{3}\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.35, size = 34, normalized size = 0.61 \begin {gather*} \frac {2}{3} \, x^{\frac {3}{2}} + \frac {3}{4} \, x^{\frac {4}{3}} + \frac {6}{7} \, x^{\frac {7}{6}} + 3 \, x + \frac {6}{5} \, x^{\frac {5}{6}} + \frac {3}{2} \, x^{\frac {2}{3}} + 2 \, \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.59, size = 32, normalized size = 0.57 \begin {gather*} \frac {2}{3} \, {\left (x + 3\right )} \sqrt {x} + \frac {3}{4} \, x^{\frac {4}{3}} + \frac {6}{7} \, x^{\frac {7}{6}} + 3 \, x + \frac {6}{5} \, x^{\frac {5}{6}} + \frac {3}{2} \, x^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 11.20, size = 51, normalized size = 0.91 \begin {gather*} \frac {6 x^{\frac {7}{6}}}{7} + \frac {6 x^{\frac {5}{6}}}{5} + \frac {3 x^{\frac {4}{3}}}{4} + \frac {3 x^{\frac {2}{3}}}{2} + \frac {2 x^{\frac {3}{2}}}{3} + 2 \sqrt {x} + 3 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.47, size = 34, normalized size = 0.61 \begin {gather*} \frac {2}{3} \, x^{\frac {3}{2}} + \frac {3}{4} \, x^{\frac {4}{3}} + \frac {6}{7} \, x^{\frac {7}{6}} + 3 \, x + \frac {6}{5} \, x^{\frac {5}{6}} + \frac {3}{2} \, x^{\frac {2}{3}} + 2 \, \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 34, normalized size = 0.61 \begin {gather*} 3\,x+2\,\sqrt {x}+\frac {3\,x^{2/3}}{2}+\frac {2\,x^{3/2}}{3}+\frac {3\,x^{4/3}}{4}+\frac {6\,x^{5/6}}{5}+\frac {6\,x^{7/6}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Chatgpt [F] Failed to verify
time = 1.00, size = 29, normalized size = 0.52 \begin {gather*} x +4 \sqrt {x}+6 x^{\frac {2}{3}}+\ln \left (x \right )-\frac {4}{\sqrt {x}}-\frac {3}{x^{\frac {2}{3}}}-\frac {3}{x^{\frac {1}{3}}} \end {gather*}
Warning: Unable to verify antiderivative.
[In]
[Out]
________________________________________________________________________________________