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 = 0.01, 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}{3} b x^{3/2}+\frac {2}{7} c x^{7/2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, 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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fricas [A] time = 1.10, 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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giac [A] time = 0.20, 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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maple [A] time = 0.00, size = 16, normalized size = 0.76 \begin {gather*} \frac {2 \left (3 c \,x^{2}+7 b \right ) x^{\frac {3}{2}}}{21} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, 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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sympy [A] time = 0.79, 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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