Optimal. Leaf size=16 \[ \frac{2 (a+b x)^{5/2}}{5 b} \]
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Rubi [A] time = 0.0013847, antiderivative size = 16, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0101099, size = 16, normalized size = 1. \[ \frac{2 (a+b x)^{5/2}}{5 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.8 \begin{align*}{\frac{2}{5\,b} \left ( bx+a \right ) ^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06051, size = 16, normalized size = 1. \begin{align*} \frac{2 \,{\left (b x + a\right )}^{\frac{5}{2}}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.45074, size = 63, normalized size = 3.94 \begin{align*} \frac{2 \,{\left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )} \sqrt{b x + a}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.069356, size = 12, normalized size = 0.75 \begin{align*} \frac{2 \left (a + b x\right )^{\frac{5}{2}}}{5 b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20759, size = 16, normalized size = 1. \begin{align*} \frac{2 \,{\left (b x + a\right )}^{\frac{5}{2}}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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