Optimal. Leaf size=16 \[ -\frac {2}{3 b (a+b x)^{3/2}} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {32} \[ -\frac {2}{3 b (a+b x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int \frac {1}{(a+b x)^{5/2}} \, dx &=-\frac {2}{3 b (a+b x)^{3/2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ -\frac {2}{3 b (a+b x)^{3/2}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.48, size = 31, normalized size = 1.94 \[ -\frac {2 \, \sqrt {b x + a}}{3 \, {\left (b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 12, normalized size = 0.75 \[ -\frac {2}{3 \, {\left (b x + a\right )}^{\frac {3}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ -\frac {2}{3 \left (b x +a \right )^{\frac {3}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 12, normalized size = 0.75 \[ -\frac {2}{3 \, {\left (b x + a\right )}^{\frac {3}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 12, normalized size = 0.75 \[ -\frac {2}{3\,b\,{\left (a+b\,x\right )}^{3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 14, normalized size = 0.88 \[ - \frac {2}{3 b \left (a + b x\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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