Optimal. Leaf size=19 \[ -\frac {2 \sqrt {a+b x}}{a \sqrt {x}} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {37} \begin {gather*} -\frac {2 \sqrt {a+b x}}{a \sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {1}{x^{3/2} \sqrt {a+b x}} \, dx &=-\frac {2 \sqrt {a+b x}}{a \sqrt {x}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \begin {gather*} -\frac {2 \sqrt {a+b x}}{a \sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 19, normalized size = 1.00 \begin {gather*} -\frac {2 \sqrt {a+b x}}{a \sqrt {x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.95, size = 15, normalized size = 0.79 \begin {gather*} -\frac {2 \, \sqrt {b x + a}}{a \sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 2.05, size = 33, normalized size = 1.74 \begin {gather*} -\frac {2 \, \sqrt {b x + a} b^{2}}{\sqrt {{\left (b x + a\right )} b - a b} a {\left | b \right |}} \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 = 0.84 \begin {gather*} -\frac {2 \sqrt {b x +a}}{a \sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 15, normalized size = 0.79 \begin {gather*} -\frac {2 \, \sqrt {b x + a}}{a \sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.35, size = 15, normalized size = 0.79 \begin {gather*} -\frac {2\,\sqrt {a+b\,x}}{a\,\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.91, size = 19, normalized size = 1.00 \begin {gather*} - \frac {2 \sqrt {b} \sqrt {\frac {a}{b x} + 1}}{a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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