Optimal. Leaf size=30 \[ \frac {a^2 x^7}{7}+\frac {1}{4} a b x^8+\frac {b^2 x^9}{9} \]
________________________________________________________________________________________
Rubi [A] time = 0.03, 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 = {1584, 43} \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 43
Rule 1584
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]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^2 \left (a x^2+b x^3\right )^2 \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.34, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{9} x^{9} b^{2} + \frac {1}{4} x^{8} b a + \frac {1}{7} x^{7} a^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, 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]
________________________________________________________________________________________
maple [A] time = 0.04, size = 25, normalized size = 0.83 \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]
________________________________________________________________________________________
maxima [A] time = 1.35, 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]
________________________________________________________________________________________
sympy [A] time = 0.07, 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]
________________________________________________________________________________________