Optimal. Leaf size=47 \[ \frac {1}{3} x^3 (a e+b d)+\frac {1}{2} a d x^2+\frac {1}{4} x^4 (b e+c d)+\frac {1}{5} c e x^5 \]
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Rubi [A] time = 0.04, antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {765} \begin {gather*} \frac {1}{3} x^3 (a e+b d)+\frac {1}{2} a d x^2+\frac {1}{4} x^4 (b e+c d)+\frac {1}{5} c e x^5 \end {gather*}
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin {align*} \int x (d+e x) \left (a+b x+c x^2\right ) \, dx &=\int \left (a d x+(b d+a e) x^2+(c d+b e) x^3+c e x^4\right ) \, dx\\ &=\frac {1}{2} a d x^2+\frac {1}{3} (b d+a e) x^3+\frac {1}{4} (c d+b e) x^4+\frac {1}{5} c e x^5\\ \end {align*}
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Mathematica [A] time = 0.01, size = 41, normalized size = 0.87 \begin {gather*} \frac {1}{60} x^2 \left (20 x (a e+b d)+30 a d+15 x^2 (b e+c d)+12 c e x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x (d+e x) \left (a+b x+c x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.32, size = 43, normalized size = 0.91 \begin {gather*} \frac {1}{5} x^{5} e c + \frac {1}{4} x^{4} d c + \frac {1}{4} x^{4} e b + \frac {1}{3} x^{3} d b + \frac {1}{3} x^{3} e a + \frac {1}{2} x^{2} d a \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 46, normalized size = 0.98 \begin {gather*} \frac {1}{5} \, c x^{5} e + \frac {1}{4} \, c d x^{4} + \frac {1}{4} \, b x^{4} e + \frac {1}{3} \, b d x^{3} + \frac {1}{3} \, a x^{3} e + \frac {1}{2} \, a d x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 40, normalized size = 0.85 \begin {gather*} \frac {c e \,x^{5}}{5}+\frac {a d \,x^{2}}{2}+\frac {\left (b e +c d \right ) x^{4}}{4}+\frac {\left (a e +b d \right ) x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 39, normalized size = 0.83 \begin {gather*} \frac {1}{5} \, c e x^{5} + \frac {1}{4} \, {\left (c d + b e\right )} x^{4} + \frac {1}{2} \, a d x^{2} + \frac {1}{3} \, {\left (b d + a e\right )} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 41, normalized size = 0.87 \begin {gather*} \frac {c\,e\,x^5}{5}+\left (\frac {b\,e}{4}+\frac {c\,d}{4}\right )\,x^4+\left (\frac {a\,e}{3}+\frac {b\,d}{3}\right )\,x^3+\frac {a\,d\,x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 42, normalized size = 0.89 \begin {gather*} \frac {a d x^{2}}{2} + \frac {c e x^{5}}{5} + x^{4} \left (\frac {b e}{4} + \frac {c d}{4}\right ) + x^{3} \left (\frac {a e}{3} + \frac {b d}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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