Optimal. Leaf size=21 \[ \frac {2}{13} b x^{13/2}+\frac {2}{17} c x^{17/2} \]
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Rubi [A]
time = 0.00, antiderivative size = 21, 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 = {14}
\begin {gather*} \frac {2}{13} b x^{13/2}+\frac {2}{17} c x^{17/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int x^{7/2} \left (b x^2+c x^4\right ) \, dx &=\int \left (b x^{11/2}+c x^{15/2}\right ) \, dx\\ &=\frac {2}{13} b x^{13/2}+\frac {2}{17} c x^{17/2}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 21, normalized size = 1.00 \begin {gather*} \frac {2}{221} \left (17 b x^{13/2}+13 c x^{17/2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 14, normalized size = 0.67
method | result | size |
derivativedivides | \(\frac {2 b \,x^{\frac {13}{2}}}{13}+\frac {2 c \,x^{\frac {17}{2}}}{17}\) | \(14\) |
default | \(\frac {2 b \,x^{\frac {13}{2}}}{13}+\frac {2 c \,x^{\frac {17}{2}}}{17}\) | \(14\) |
gosper | \(\frac {2 x^{\frac {13}{2}} \left (13 c \,x^{2}+17 b \right )}{221}\) | \(16\) |
trager | \(\frac {2 x^{\frac {13}{2}} \left (13 c \,x^{2}+17 b \right )}{221}\) | \(16\) |
risch | \(\frac {2 x^{\frac {13}{2}} \left (13 c \,x^{2}+17 b \right )}{221}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{17} \, c x^{\frac {17}{2}} + \frac {2}{13} \, b x^{\frac {13}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 18, normalized size = 0.86 \begin {gather*} \frac {2}{221} \, {\left (13 \, c x^{8} + 17 \, b x^{6}\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.77, size = 19, normalized size = 0.90 \begin {gather*} \frac {2 b x^{\frac {13}{2}}}{13} + \frac {2 c x^{\frac {17}{2}}}{17} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.69, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{17} \, c x^{\frac {17}{2}} + \frac {2}{13} \, b x^{\frac {13}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 15, normalized size = 0.71 \begin {gather*} \frac {2\,x^{13/2}\,\left (13\,c\,x^2+17\,b\right )}{221} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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