Optimal. Leaf size=30 \[ \frac {a^2 x^7}{7}+\frac {1}{4} a b x^8+\frac {b^2 x^9}{9} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {1598, 45}
\begin {gather*} \frac {a^2 x^7}{7}+\frac {1}{4} a b x^8+\frac {b^2 x^9}{9} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 45
Rule 1598
Rubi steps
\begin {align*} \int x^2 \left (a x^2+b x^3\right )^2 \, dx &=\int x^6 (a+b x)^2 \, dx\\ &=\int \left (a^2 x^6+2 a b x^7+b^2 x^8\right ) \, dx\\ &=\frac {a^2 x^7}{7}+\frac {1}{4} a b x^8+\frac {b^2 x^9}{9}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} \frac {a^2 x^7}{7}+\frac {1}{4} a b x^8+\frac {b^2 x^9}{9} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.43, size = 25, normalized size = 0.83
method | result | size |
gosper | \(\frac {x^{7} \left (28 b^{2} x^{2}+63 a b x +36 a^{2}\right )}{252}\) | \(25\) |
default | \(\frac {1}{7} a^{2} x^{7}+\frac {1}{4} a b \,x^{8}+\frac {1}{9} b^{2} x^{9}\) | \(25\) |
norman | \(\frac {1}{7} a^{2} x^{7}+\frac {1}{4} a b \,x^{8}+\frac {1}{9} b^{2} x^{9}\) | \(25\) |
risch | \(\frac {1}{7} a^{2} x^{7}+\frac {1}{4} a b \,x^{8}+\frac {1}{9} b^{2} x^{9}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{9} \, b^{2} x^{9} + \frac {1}{4} \, a b x^{8} + \frac {1}{7} \, a^{2} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.28, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{9} \, b^{2} x^{9} + \frac {1}{4} \, a b x^{8} + \frac {1}{7} \, a^{2} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 24, normalized size = 0.80 \begin {gather*} \frac {a^{2} x^{7}}{7} + \frac {a b x^{8}}{4} + \frac {b^{2} x^{9}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.44, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{9} \, b^{2} x^{9} + \frac {1}{4} \, a b x^{8} + \frac {1}{7} \, a^{2} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 24, normalized size = 0.80 \begin {gather*} \frac {a^2\,x^7}{7}+\frac {a\,b\,x^8}{4}+\frac {b^2\,x^9}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________