Optimal. Leaf size=30 \[ \frac {a^2 x^2}{2}+\frac {2}{5} a b x^5+\frac {b^2 x^8}{8} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {276}
\begin {gather*} \frac {a^2 x^2}{2}+\frac {2}{5} a b x^5+\frac {b^2 x^8}{8} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 276
Rubi steps
\begin {align*} \int x \left (a+b x^3\right )^2 \, dx &=\int \left (a^2 x+2 a b x^4+b^2 x^7\right ) \, dx\\ &=\frac {a^2 x^2}{2}+\frac {2}{5} a b x^5+\frac {b^2 x^8}{8}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} \frac {a^2 x^2}{2}+\frac {2}{5} a b x^5+\frac {b^2 x^8}{8} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.14, size = 25, normalized size = 0.83
method | result | size |
gosper | \(\frac {1}{2} a^{2} x^{2}+\frac {2}{5} a b \,x^{5}+\frac {1}{8} b^{2} x^{8}\) | \(25\) |
default | \(\frac {1}{2} a^{2} x^{2}+\frac {2}{5} a b \,x^{5}+\frac {1}{8} b^{2} x^{8}\) | \(25\) |
norman | \(\frac {1}{2} a^{2} x^{2}+\frac {2}{5} a b \,x^{5}+\frac {1}{8} b^{2} x^{8}\) | \(25\) |
risch | \(\frac {1}{2} a^{2} x^{2}+\frac {2}{5} a b \,x^{5}+\frac {1}{8} b^{2} x^{8}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{8} \, b^{2} x^{8} + \frac {2}{5} \, a b x^{5} + \frac {1}{2} \, a^{2} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.33, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{8} \, b^{2} x^{8} + \frac {2}{5} \, a b x^{5} + \frac {1}{2} \, a^{2} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 26, normalized size = 0.87 \begin {gather*} \frac {a^{2} x^{2}}{2} + \frac {2 a b x^{5}}{5} + \frac {b^{2} x^{8}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 2.40, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{8} \, b^{2} x^{8} + \frac {2}{5} \, a b x^{5} + \frac {1}{2} \, a^{2} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 24, normalized size = 0.80 \begin {gather*} \frac {a^2\,x^2}{2}+\frac {2\,a\,b\,x^5}{5}+\frac {b^2\,x^8}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________