Optimal. Leaf size=28 \[ \frac {a x^4}{4}+a x+\frac {b x^5}{5}+\frac {b x^2}{2} \]
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Rubi [A] time = 0.02, antiderivative size = 28, 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 = {771} \begin {gather*} \frac {a x^4}{4}+a x+\frac {b x^5}{5}+\frac {b x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin {align*} \int (1+x) (a+b x) \left (1-x+x^2\right ) \, dx &=\int \left (a+b x+a x^3+b x^4\right ) \, dx\\ &=a x+\frac {b x^2}{2}+\frac {a x^4}{4}+\frac {b x^5}{5}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 28, normalized size = 1.00 \begin {gather*} \frac {a x^4}{4}+a x+\frac {b x^5}{5}+\frac {b x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1+x) (a+b x) \left (1-x+x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.34, size = 22, normalized size = 0.79 \begin {gather*} \frac {1}{5} x^{5} b + \frac {1}{4} x^{4} a + \frac {1}{2} x^{2} b + x a \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 22, normalized size = 0.79 \begin {gather*} \frac {1}{5} \, b x^{5} + \frac {1}{4} \, a x^{4} + \frac {1}{2} \, b x^{2} + a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 23, normalized size = 0.82 \begin {gather*} \frac {1}{5} b \,x^{5}+\frac {1}{4} a \,x^{4}+\frac {1}{2} b \,x^{2}+a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 22, normalized size = 0.79 \begin {gather*} \frac {1}{5} \, b x^{5} + \frac {1}{4} \, a x^{4} + \frac {1}{2} \, b x^{2} + a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 22, normalized size = 0.79 \begin {gather*} \frac {b\,x^5}{5}+\frac {a\,x^4}{4}+\frac {b\,x^2}{2}+a\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 22, normalized size = 0.79 \begin {gather*} \frac {a x^{4}}{4} + a x + \frac {b x^{5}}{5} + \frac {b x^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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