Optimal. Leaf size=21 \[ \frac {2}{3} b x^{3/2}+\frac {2}{7} c x^{7/2} \]
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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}{3} b x^{3/2}+\frac {2}{7} c x^{7/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {b x^2+c x^4}{x^{3/2}} \, dx &=\int \left (b \sqrt {x}+c x^{5/2}\right ) \, dx\\ &=\frac {2}{3} b x^{3/2}+\frac {2}{7} c x^{7/2}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 21, normalized size = 1.00 \begin {gather*} \frac {2}{21} \left (7 b x^{3/2}+3 c x^{7/2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 14, normalized size = 0.67
method | result | size |
derivativedivides | \(\frac {2 b \,x^{\frac {3}{2}}}{3}+\frac {2 c \,x^{\frac {7}{2}}}{7}\) | \(14\) |
default | \(\frac {2 b \,x^{\frac {3}{2}}}{3}+\frac {2 c \,x^{\frac {7}{2}}}{7}\) | \(14\) |
gosper | \(\frac {2 x^{\frac {3}{2}} \left (3 c \,x^{2}+7 b \right )}{21}\) | \(16\) |
trager | \(\frac {2 x^{\frac {3}{2}} \left (3 c \,x^{2}+7 b \right )}{21}\) | \(16\) |
risch | \(\frac {2 x^{\frac {3}{2}} \left (3 c \,x^{2}+7 b \right )}{21}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{7} \, c x^{\frac {7}{2}} + \frac {2}{3} \, b x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 16, normalized size = 0.76 \begin {gather*} \frac {2}{21} \, {\left (3 \, c x^{3} + 7 \, b x\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.18, size = 19, normalized size = 0.90 \begin {gather*} \frac {2 b x^{\frac {3}{2}}}{3} + \frac {2 c x^{\frac {7}{2}}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.72, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{7} \, c x^{\frac {7}{2}} + \frac {2}{3} \, b x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 15, normalized size = 0.71 \begin {gather*} \frac {2\,x^{3/2}\,\left (3\,c\,x^2+7\,b\right )}{21} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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