Optimal. Leaf size=17 \[ \frac{x^2}{2 a (a+b x)^2} \]
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Rubi [A] time = 0.0016454, antiderivative size = 17, 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 = {37} \[ \frac{x^2}{2 a (a+b x)^2} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{x}{(a+b x)^3} \, dx &=\frac{x^2}{2 a (a+b x)^2}\\ \end{align*}
Mathematica [A] time = 0.0078628, size = 20, normalized size = 1.18 \[ -\frac{a+2 b x}{2 b^2 (a+b x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 27, normalized size = 1.6 \begin{align*} -{\frac{1}{{b}^{2} \left ( bx+a \right ) }}+{\frac{a}{2\,{b}^{2} \left ( bx+a \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.989177, size = 43, normalized size = 2.53 \begin{align*} -\frac{2 \, b x + a}{2 \,{\left (b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.53172, size = 68, normalized size = 4. \begin{align*} -\frac{2 \, b x + a}{2 \,{\left (b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.429561, size = 32, normalized size = 1.88 \begin{align*} - \frac{a + 2 b x}{2 a^{2} b^{2} + 4 a b^{3} x + 2 b^{4} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2015, size = 24, normalized size = 1.41 \begin{align*} -\frac{2 \, b x + a}{2 \,{\left (b x + a\right )}^{2} b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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