Optimal. Leaf size=37 \[ \frac {1}{4} a A x^4+\frac {1}{5} a B x^5+\frac {1}{6} A c x^6+\frac {1}{7} B c x^7 \]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {766} \begin {gather*} \frac {1}{4} a A x^4+\frac {1}{5} a B x^5+\frac {1}{6} A c x^6+\frac {1}{7} B c x^7 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 766
Rubi steps
\begin {align*} \int x^3 (A+B x) \left (a+c x^2\right ) \, dx &=\int \left (a A x^3+a B x^4+A c x^5+B c x^6\right ) \, dx\\ &=\frac {1}{4} a A x^4+\frac {1}{5} a B x^5+\frac {1}{6} A c x^6+\frac {1}{7} B c x^7\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 37, normalized size = 1.00 \begin {gather*} \frac {1}{4} a A x^4+\frac {1}{5} a B x^5+\frac {1}{6} A c x^6+\frac {1}{7} B c x^7 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^3 (A+B x) \left (a+c x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.35, size = 29, normalized size = 0.78 \begin {gather*} \frac {1}{7} x^{7} c B + \frac {1}{6} x^{6} c A + \frac {1}{5} x^{5} a B + \frac {1}{4} x^{4} a A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 29, normalized size = 0.78 \begin {gather*} \frac {1}{7} \, B c x^{7} + \frac {1}{6} \, A c x^{6} + \frac {1}{5} \, B a x^{5} + \frac {1}{4} \, A a x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 30, normalized size = 0.81 \begin {gather*} \frac {1}{7} B c \,x^{7}+\frac {1}{6} A c \,x^{6}+\frac {1}{5} B a \,x^{5}+\frac {1}{4} A a \,x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.61, size = 29, normalized size = 0.78 \begin {gather*} \frac {1}{7} \, B c x^{7} + \frac {1}{6} \, A c x^{6} + \frac {1}{5} \, B a x^{5} + \frac {1}{4} \, A a x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 29, normalized size = 0.78 \begin {gather*} \frac {B\,c\,x^7}{7}+\frac {A\,c\,x^6}{6}+\frac {B\,a\,x^5}{5}+\frac {A\,a\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 32, normalized size = 0.86 \begin {gather*} \frac {A a x^{4}}{4} + \frac {A c x^{6}}{6} + \frac {B a x^{5}}{5} + \frac {B c x^{7}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________