Optimal. Leaf size=73 \[ \frac {1}{7} x^7 \left (e (a e+2 b d)+c d^2\right )+\frac {1}{4} d x^4 (2 a e+b d)+a d^2 x+\frac {1}{10} e x^{10} (b e+2 c d)+\frac {1}{13} c e^2 x^{13} \]
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Rubi [A] time = 0.06, antiderivative size = 73, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {1407} \begin {gather*} \frac {1}{7} x^7 \left (e (a e+2 b d)+c d^2\right )+\frac {1}{4} d x^4 (2 a e+b d)+a d^2 x+\frac {1}{10} e x^{10} (b e+2 c d)+\frac {1}{13} c e^2 x^{13} \end {gather*}
Antiderivative was successfully verified.
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Rule 1407
Rubi steps
\begin {align*} \int \left (d+e x^3\right )^2 \left (a+b x^3+c x^6\right ) \, dx &=\int \left (a d^2+d (b d+2 a e) x^3+\left (c d^2+e (2 b d+a e)\right ) x^6+e (2 c d+b e) x^9+c e^2 x^{12}\right ) \, dx\\ &=a d^2 x+\frac {1}{4} d (b d+2 a e) x^4+\frac {1}{7} \left (c d^2+e (2 b d+a e)\right ) x^7+\frac {1}{10} e (2 c d+b e) x^{10}+\frac {1}{13} c e^2 x^{13}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 73, normalized size = 1.00 \begin {gather*} \frac {1}{7} x^7 \left (a e^2+2 b d e+c d^2\right )+\frac {1}{4} d x^4 (2 a e+b d)+a d^2 x+\frac {1}{10} e x^{10} (b e+2 c d)+\frac {1}{13} c e^2 x^{13} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (d+e x^3\right )^2 \left (a+b x^3+c x^6\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.91, size = 76, normalized size = 1.04 \begin {gather*} \frac {1}{13} x^{13} e^{2} c + \frac {1}{5} x^{10} e d c + \frac {1}{10} x^{10} e^{2} b + \frac {1}{7} x^{7} d^{2} c + \frac {2}{7} x^{7} e d b + \frac {1}{7} x^{7} e^{2} a + \frac {1}{4} x^{4} d^{2} b + \frac {1}{2} x^{4} e d a + x d^{2} a \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 76, normalized size = 1.04 \begin {gather*} \frac {1}{13} \, c x^{13} e^{2} + \frac {1}{5} \, c d x^{10} e + \frac {1}{10} \, b x^{10} e^{2} + \frac {1}{7} \, c d^{2} x^{7} + \frac {2}{7} \, b d x^{7} e + \frac {1}{7} \, a x^{7} e^{2} + \frac {1}{4} \, b d^{2} x^{4} + \frac {1}{2} \, a d x^{4} e + a d^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 70, normalized size = 0.96 \begin {gather*} \frac {c \,e^{2} x^{13}}{13}+\frac {\left (b \,e^{2}+2 c d e \right ) x^{10}}{10}+\frac {\left (a \,e^{2}+2 d e b +c \,d^{2}\right ) x^{7}}{7}+a \,d^{2} x +\frac {\left (2 d e a +b \,d^{2}\right ) x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.75, size = 69, normalized size = 0.95 \begin {gather*} \frac {1}{13} \, c e^{2} x^{13} + \frac {1}{10} \, {\left (2 \, c d e + b e^{2}\right )} x^{10} + \frac {1}{7} \, {\left (c d^{2} + 2 \, b d e + a e^{2}\right )} x^{7} + \frac {1}{4} \, {\left (b d^{2} + 2 \, a d e\right )} x^{4} + a d^{2} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 70, normalized size = 0.96 \begin {gather*} x^7\,\left (\frac {c\,d^2}{7}+\frac {2\,b\,d\,e}{7}+\frac {a\,e^2}{7}\right )+x^4\,\left (\frac {b\,d^2}{4}+\frac {a\,e\,d}{2}\right )+x^{10}\,\left (\frac {b\,e^2}{10}+\frac {c\,d\,e}{5}\right )+\frac {c\,e^2\,x^{13}}{13}+a\,d^2\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 75, normalized size = 1.03 \begin {gather*} a d^{2} x + \frac {c e^{2} x^{13}}{13} + x^{10} \left (\frac {b e^{2}}{10} + \frac {c d e}{5}\right ) + x^{7} \left (\frac {a e^{2}}{7} + \frac {2 b d e}{7} + \frac {c d^{2}}{7}\right ) + x^{4} \left (\frac {a d e}{2} + \frac {b d^{2}}{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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