Optimal. Leaf size=17 \[ -\frac {2 a}{\sqrt {x}}+2 b \sqrt {x} \]
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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45}
\begin {gather*} 2 b \sqrt {x}-\frac {2 a}{\sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {a+b x}{x^{3/2}} \, dx &=\int \left (\frac {a}{x^{3/2}}+\frac {b}{\sqrt {x}}\right ) \, dx\\ &=-\frac {2 a}{\sqrt {x}}+2 b \sqrt {x}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 0.76 \begin {gather*} -\frac {2 (a-b x)}{\sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 14, normalized size = 0.82
method | result | size |
gosper | \(-\frac {2 \left (-b x +a \right )}{\sqrt {x}}\) | \(12\) |
trager | \(-\frac {2 \left (-b x +a \right )}{\sqrt {x}}\) | \(12\) |
risch | \(-\frac {2 \left (-b x +a \right )}{\sqrt {x}}\) | \(12\) |
derivativedivides | \(-\frac {2 a}{\sqrt {x}}+2 b \sqrt {x}\) | \(14\) |
default | \(-\frac {2 a}{\sqrt {x}}+2 b \sqrt {x}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 13, normalized size = 0.76 \begin {gather*} 2 \, b \sqrt {x} - \frac {2 \, a}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 12, normalized size = 0.71 \begin {gather*} \frac {2 \, {\left (b x - a\right )}}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 15, normalized size = 0.88 \begin {gather*} - \frac {2 a}{\sqrt {x}} + 2 b \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.55, size = 13, normalized size = 0.76 \begin {gather*} 2 \, b \sqrt {x} - \frac {2 \, a}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 11, normalized size = 0.65 \begin {gather*} -\frac {2\,\left (a-b\,x\right )}{\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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