Optimal. Leaf size=19 \[ \frac {a x^5}{5}+\frac {3}{16} b x^{16/3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14} \[ \frac {a x^5}{5}+\frac {3}{16} b x^{16/3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {align*} \int \left (a+b \sqrt [3]{x}\right ) x^4 \, dx &=\int \left (a x^4+b x^{13/3}\right ) \, dx\\ &=\frac {a x^5}{5}+\frac {3}{16} b x^{16/3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 19, normalized size = 1.00 \[ \frac {a x^5}{5}+\frac {3}{16} b x^{16/3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.49, size = 13, normalized size = 0.68 \[ \frac {3}{16} \, b x^{\frac {16}{3}} + \frac {1}{5} \, a x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 13, normalized size = 0.68 \[ \frac {3}{16} \, b x^{\frac {16}{3}} + \frac {1}{5} \, a x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 14, normalized size = 0.74 \[ \frac {3 b \,x^{\frac {16}{3}}}{16}+\frac {a \,x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.82, size = 251, normalized size = 13.21 \[ \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{16}}{16 \, b^{15}} - \frac {14 \, {\left (b x^{\frac {1}{3}} + a\right )}^{15} a}{5 \, b^{15}} + \frac {39 \, {\left (b x^{\frac {1}{3}} + a\right )}^{14} a^{2}}{2 \, b^{15}} - \frac {84 \, {\left (b x^{\frac {1}{3}} + a\right )}^{13} a^{3}}{b^{15}} + \frac {1001 \, {\left (b x^{\frac {1}{3}} + a\right )}^{12} a^{4}}{4 \, b^{15}} - \frac {546 \, {\left (b x^{\frac {1}{3}} + a\right )}^{11} a^{5}}{b^{15}} + \frac {9009 \, {\left (b x^{\frac {1}{3}} + a\right )}^{10} a^{6}}{10 \, b^{15}} - \frac {1144 \, {\left (b x^{\frac {1}{3}} + a\right )}^{9} a^{7}}{b^{15}} + \frac {9009 \, {\left (b x^{\frac {1}{3}} + a\right )}^{8} a^{8}}{8 \, b^{15}} - \frac {858 \, {\left (b x^{\frac {1}{3}} + a\right )}^{7} a^{9}}{b^{15}} + \frac {1001 \, {\left (b x^{\frac {1}{3}} + a\right )}^{6} a^{10}}{2 \, b^{15}} - \frac {1092 \, {\left (b x^{\frac {1}{3}} + a\right )}^{5} a^{11}}{5 \, b^{15}} + \frac {273 \, {\left (b x^{\frac {1}{3}} + a\right )}^{4} a^{12}}{4 \, b^{15}} - \frac {14 \, {\left (b x^{\frac {1}{3}} + a\right )}^{3} a^{13}}{b^{15}} + \frac {3 \, {\left (b x^{\frac {1}{3}} + a\right )}^{2} a^{14}}{2 \, b^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 13, normalized size = 0.68 \[ \frac {a\,x^5}{5}+\frac {3\,b\,x^{16/3}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 1.75, size = 15, normalized size = 0.79 \[ \frac {a x^{5}}{5} + \frac {3 b x^{\frac {16}{3}}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________