Optimal. Leaf size=103 \[ \frac {1}{10} e x^{10} \left (e (a e+3 b d)+3 c d^2\right )+\frac {1}{7} d x^7 \left (3 e (a e+b d)+c d^2\right )+\frac {1}{4} d^2 x^4 (3 a e+b d)+a d^3 x+\frac {1}{13} e^2 x^{13} (b e+3 c d)+\frac {1}{16} c e^3 x^{16} \]
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Rubi [A] time = 0.10, antiderivative size = 103, 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} \[ \frac {1}{10} e x^{10} \left (e (a e+3 b d)+3 c d^2\right )+\frac {1}{7} d x^7 \left (3 e (a e+b d)+c d^2\right )+\frac {1}{4} d^2 x^4 (3 a e+b d)+a d^3 x+\frac {1}{13} e^2 x^{13} (b e+3 c d)+\frac {1}{16} c e^3 x^{16} \]
Antiderivative was successfully verified.
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Rule 1407
Rubi steps
\begin {align*} \int \left (d+e x^3\right )^3 \left (a+b x^3+c x^6\right ) \, dx &=\int \left (a d^3+d^2 (b d+3 a e) x^3+d \left (c d^2+3 e (b d+a e)\right ) x^6+e \left (3 c d^2+e (3 b d+a e)\right ) x^9+e^2 (3 c d+b e) x^{12}+c e^3 x^{15}\right ) \, dx\\ &=a d^3 x+\frac {1}{4} d^2 (b d+3 a e) x^4+\frac {1}{7} d \left (c d^2+3 e (b d+a e)\right ) x^7+\frac {1}{10} e \left (3 c d^2+e (3 b d+a e)\right ) x^{10}+\frac {1}{13} e^2 (3 c d+b e) x^{13}+\frac {1}{16} c e^3 x^{16}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 104, normalized size = 1.01 \[ \frac {1}{10} e x^{10} \left (a e^2+3 b d e+3 c d^2\right )+\frac {1}{7} d x^7 \left (3 a e^2+3 b d e+c d^2\right )+\frac {1}{4} d^2 x^4 (3 a e+b d)+a d^3 x+\frac {1}{13} e^2 x^{13} (b e+3 c d)+\frac {1}{16} c e^3 x^{16} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 112, normalized size = 1.09 \[ \frac {1}{16} x^{16} e^{3} c + \frac {3}{13} x^{13} e^{2} d c + \frac {1}{13} x^{13} e^{3} b + \frac {3}{10} x^{10} e d^{2} c + \frac {3}{10} x^{10} e^{2} d b + \frac {1}{10} x^{10} e^{3} a + \frac {1}{7} x^{7} d^{3} c + \frac {3}{7} x^{7} e d^{2} b + \frac {3}{7} x^{7} e^{2} d a + \frac {1}{4} x^{4} d^{3} b + \frac {3}{4} x^{4} e d^{2} a + x d^{3} a \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 109, normalized size = 1.06 \[ \frac {1}{16} \, c x^{16} e^{3} + \frac {3}{13} \, c d x^{13} e^{2} + \frac {1}{13} \, b x^{13} e^{3} + \frac {3}{10} \, c d^{2} x^{10} e + \frac {3}{10} \, b d x^{10} e^{2} + \frac {1}{10} \, a x^{10} e^{3} + \frac {1}{7} \, c d^{3} x^{7} + \frac {3}{7} \, b d^{2} x^{7} e + \frac {3}{7} \, a d x^{7} e^{2} + \frac {1}{4} \, b d^{3} x^{4} + \frac {3}{4} \, a d^{2} x^{4} e + a d^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 103, normalized size = 1.00 \[ \frac {c \,e^{3} x^{16}}{16}+\frac {\left (e^{3} b +3 c d \,e^{2}\right ) x^{13}}{13}+\frac {\left (e^{3} a +3 b d \,e^{2}+3 d^{2} e c \right ) x^{10}}{10}+\frac {\left (3 a d \,e^{2}+3 b \,d^{2} e +c \,d^{3}\right ) x^{7}}{7}+a \,d^{3} x +\frac {\left (3 a \,d^{2} e +b \,d^{3}\right ) x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 102, normalized size = 0.99 \[ \frac {1}{16} \, c e^{3} x^{16} + \frac {1}{13} \, {\left (3 \, c d e^{2} + b e^{3}\right )} x^{13} + \frac {1}{10} \, {\left (3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right )} x^{10} + \frac {1}{7} \, {\left (c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right )} x^{7} + a d^{3} x + \frac {1}{4} \, {\left (b d^{3} + 3 \, a d^{2} e\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 102, normalized size = 0.99 \[ x^4\,\left (\frac {b\,d^3}{4}+\frac {3\,a\,e\,d^2}{4}\right )+x^{13}\,\left (\frac {b\,e^3}{13}+\frac {3\,c\,d\,e^2}{13}\right )+x^7\,\left (\frac {c\,d^3}{7}+\frac {3\,b\,d^2\,e}{7}+\frac {3\,a\,d\,e^2}{7}\right )+x^{10}\,\left (\frac {3\,c\,d^2\,e}{10}+\frac {3\,b\,d\,e^2}{10}+\frac {a\,e^3}{10}\right )+\frac {c\,e^3\,x^{16}}{16}+a\,d^3\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 117, normalized size = 1.14 \[ a d^{3} x + \frac {c e^{3} x^{16}}{16} + x^{13} \left (\frac {b e^{3}}{13} + \frac {3 c d e^{2}}{13}\right ) + x^{10} \left (\frac {a e^{3}}{10} + \frac {3 b d e^{2}}{10} + \frac {3 c d^{2} e}{10}\right ) + x^{7} \left (\frac {3 a d e^{2}}{7} + \frac {3 b d^{2} e}{7} + \frac {c d^{3}}{7}\right ) + x^{4} \left (\frac {3 a d^{2} e}{4} + \frac {b d^{3}}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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