Optimal. Leaf size=19 \[ -\frac {2 b}{\sqrt {x}}+\frac {2}{3} c x^{3/2} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, 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} c x^{3/2}-\frac {2 b}{\sqrt {x}} \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^{7/2}} \, dx &=\int \left (\frac {b}{x^{3/2}}+c \sqrt {x}\right ) \, dx\\ &=-\frac {2 b}{\sqrt {x}}+\frac {2}{3} c x^{3/2}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} -\frac {2 \left (3 b-c x^2\right )}{3 \sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 14, normalized size = 0.74
method | result | size |
derivativedivides | \(\frac {2 c \,x^{\frac {3}{2}}}{3}-\frac {2 b}{\sqrt {x}}\) | \(14\) |
default | \(\frac {2 c \,x^{\frac {3}{2}}}{3}-\frac {2 b}{\sqrt {x}}\) | \(14\) |
gosper | \(-\frac {2 \left (-c \,x^{2}+3 b \right )}{3 \sqrt {x}}\) | \(16\) |
trager | \(-\frac {2 \left (-c \,x^{2}+3 b \right )}{3 \sqrt {x}}\) | \(16\) |
risch | \(-\frac {2 \left (-c \,x^{2}+3 b \right )}{3 \sqrt {x}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{3} \, c x^{\frac {3}{2}} - \frac {2 \, b}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 14, normalized size = 0.74 \begin {gather*} \frac {2 \, {\left (c x^{2} - 3 \, b\right )}}{3 \, \sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.37, size = 17, normalized size = 0.89 \begin {gather*} - \frac {2 b}{\sqrt {x}} + \frac {2 c x^{\frac {3}{2}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.78, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{3} \, c x^{\frac {3}{2}} - \frac {2 \, b}{\sqrt {x}} \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 = 0.79 \begin {gather*} -\frac {6\,b-2\,c\,x^2}{3\,\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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