Optimal. Leaf size=44 \[ a x+\frac {b x^2}{2}+\frac {a x^4}{2}+\frac {2 b x^5}{5}+\frac {a x^7}{7}+\frac {b x^8}{8} \]
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Rubi [A]
time = 0.02, antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {785}
\begin {gather*} \frac {a x^7}{7}+\frac {a x^4}{2}+a x+\frac {b x^8}{8}+\frac {2 b x^5}{5}+\frac {b x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 785
Rubi steps
\begin {align*} \int (1+x)^2 (a+b x) \left (1-x+x^2\right )^2 \, dx &=\int \left (a+b x+2 a x^3+2 b x^4+a x^6+b x^7\right ) \, dx\\ &=a x+\frac {b x^2}{2}+\frac {a x^4}{2}+\frac {2 b x^5}{5}+\frac {a x^7}{7}+\frac {b x^8}{8}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 44, normalized size = 1.00 \begin {gather*} a x+\frac {b x^2}{2}+\frac {a x^4}{2}+\frac {2 b x^5}{5}+\frac {a x^7}{7}+\frac {b x^8}{8} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 35, normalized size = 0.80
method | result | size |
gosper | \(a x +\frac {1}{2} b \,x^{2}+\frac {1}{2} a \,x^{4}+\frac {2}{5} b \,x^{5}+\frac {1}{7} a \,x^{7}+\frac {1}{8} b \,x^{8}\) | \(35\) |
default | \(a x +\frac {1}{2} b \,x^{2}+\frac {1}{2} a \,x^{4}+\frac {2}{5} b \,x^{5}+\frac {1}{7} a \,x^{7}+\frac {1}{8} b \,x^{8}\) | \(35\) |
norman | \(a x +\frac {1}{2} b \,x^{2}+\frac {1}{2} a \,x^{4}+\frac {2}{5} b \,x^{5}+\frac {1}{7} a \,x^{7}+\frac {1}{8} b \,x^{8}\) | \(35\) |
risch | \(a x +\frac {1}{2} b \,x^{2}+\frac {1}{2} a \,x^{4}+\frac {2}{5} b \,x^{5}+\frac {1}{7} a \,x^{7}+\frac {1}{8} b \,x^{8}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 34, normalized size = 0.77 \begin {gather*} \frac {1}{8} \, b x^{8} + \frac {1}{7} \, a x^{7} + \frac {2}{5} \, b x^{5} + \frac {1}{2} \, 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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Fricas [A]
time = 3.46, size = 34, normalized size = 0.77 \begin {gather*} \frac {1}{8} \, b x^{8} + \frac {1}{7} \, a x^{7} + \frac {2}{5} \, b x^{5} + \frac {1}{2} \, 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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Sympy [A]
time = 0.01, size = 37, normalized size = 0.84 \begin {gather*} \frac {a x^{7}}{7} + \frac {a x^{4}}{2} + a x + \frac {b x^{8}}{8} + \frac {2 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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Giac [A]
time = 1.38, size = 34, normalized size = 0.77 \begin {gather*} \frac {1}{8} \, b x^{8} + \frac {1}{7} \, a x^{7} + \frac {2}{5} \, b x^{5} + \frac {1}{2} \, 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 = 0.02, size = 34, normalized size = 0.77 \begin {gather*} \frac {b\,x^8}{8}+\frac {a\,x^7}{7}+\frac {2\,b\,x^5}{5}+\frac {a\,x^4}{2}+\frac {b\,x^2}{2}+a\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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