Optimal. Leaf size=17 \[ \frac {x^2}{2 a (a+b x)^2} \]
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Rubi [A] time = 0.00, antiderivative size = 17, 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 = {37} \begin {gather*} \frac {x^2}{2 a (a+b x)^2} \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.18 \begin {gather*} -\frac {a+2 b x}{2 b^2 (a+b x)^2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{(a+b x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 1.21, size = 32, normalized size = 1.88 \begin {gather*} -\frac {2 \, b x + a}{2 \, {\left (b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.14, size = 18, normalized size = 1.06 \begin {gather*} -\frac {2 \, b x + a}{2 \, {\left (b x + a\right )}^{2} b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 27, normalized size = 1.59 \begin {gather*} \frac {a}{2 \left (b x +a \right )^{2} b^{2}}-\frac {1}{\left (b x +a \right ) b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.39, size = 32, normalized size = 1.88 \begin {gather*} -\frac {2 \, b x + a}{2 \, {\left (b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 32, normalized size = 1.88 \begin {gather*} -\frac {\frac {a}{2\,b^2}+\frac {x}{b}}{a^2+2\,a\,b\,x+b^2\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.20, size = 32, normalized size = 1.88 \begin {gather*} \frac {- a - 2 b x}{2 a^{2} b^{2} + 4 a b^{3} x + 2 b^{4} x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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