Optimal. Leaf size=25 \[ \frac {a x^3}{3}+\frac {b x^5}{5}+\frac {c x^7}{7} \]
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Rubi [A]
time = 0.00, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {14}
\begin {gather*} \frac {a x^3}{3}+\frac {b x^5}{5}+\frac {c x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int x^2 \left (a+b x^2+c x^4\right ) \, dx &=\int \left (a x^2+b x^4+c x^6\right ) \, dx\\ &=\frac {a x^3}{3}+\frac {b x^5}{5}+\frac {c x^7}{7}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 25, normalized size = 1.00 \begin {gather*} \frac {a x^3}{3}+\frac {b x^5}{5}+\frac {c x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 20, normalized size = 0.80
method | result | size |
gosper | \(\frac {1}{3} a \,x^{3}+\frac {1}{5} b \,x^{5}+\frac {1}{7} c \,x^{7}\) | \(20\) |
default | \(\frac {1}{3} a \,x^{3}+\frac {1}{5} b \,x^{5}+\frac {1}{7} c \,x^{7}\) | \(20\) |
norman | \(\frac {1}{3} a \,x^{3}+\frac {1}{5} b \,x^{5}+\frac {1}{7} c \,x^{7}\) | \(20\) |
risch | \(\frac {1}{3} a \,x^{3}+\frac {1}{5} b \,x^{5}+\frac {1}{7} c \,x^{7}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{7} \, c x^{7} + \frac {1}{5} \, b x^{5} + \frac {1}{3} \, a x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{7} \, c x^{7} + \frac {1}{5} \, b x^{5} + \frac {1}{3} \, a x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 19, normalized size = 0.76 \begin {gather*} \frac {a x^{3}}{3} + \frac {b x^{5}}{5} + \frac {c x^{7}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.90, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{7} \, c x^{7} + \frac {1}{5} \, b x^{5} + \frac {1}{3} \, a x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 19, normalized size = 0.76 \begin {gather*} \frac {c\,x^7}{7}+\frac {b\,x^5}{5}+\frac {a\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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