Optimal. Leaf size=16 \[ \frac {2 (a+b x)^{5/2}}{5 b} \]
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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} \[ \frac {2 (a+b x)^{5/2}}{5 b} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int (a+b x)^{3/2} \, dx &=\frac {2 (a+b x)^{5/2}}{5 b}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \[ \frac {2 (a+b x)^{5/2}}{5 b} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.44, size = 28, normalized size = 1.75 \[ \frac {2 \, {\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )} \sqrt {b x + a}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.13, size = 58, normalized size = 3.62 \[ \frac {2 \, {\left (3 \, {\left (b x + a\right )}^{\frac {5}{2}} - 10 \, {\left (b x + a\right )}^{\frac {3}{2}} a + 30 \, \sqrt {b x + a} a^{2} + 10 \, {\left ({\left (b x + a\right )}^{\frac {3}{2}} - 3 \, \sqrt {b x + a} a\right )} a\right )}}{15 \, b} \]
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 \[ \frac {2 \left (b x +a \right )^{\frac {5}{2}}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 12, normalized size = 0.75 \[ \frac {2 \, {\left (b x + a\right )}^{\frac {5}{2}}}{5 \, b} \]
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 \[ \frac {2\,{\left (a+b\,x\right )}^{5/2}}{5\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 12, normalized size = 0.75 \[ \frac {2 \left (a + b x\right )^{\frac {5}{2}}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
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