Optimal. Leaf size=10 \[ \frac {x}{(a-b x)^2} \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {627, 34} \begin {gather*} \frac {x}{(a-b x)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 34
Rule 627
Rubi steps
\begin {align*} \int \frac {(a+b x)^4}{\left (a^2-b^2 x^2\right )^3} \, dx &=\int \frac {a+b x}{(a-b x)^3} \, dx\\ &=\frac {x}{(a-b x)^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {x}{(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 {(a+b x)^4}{\left (a^2-b^2 x^2\right )^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.38, size = 20, normalized size = 2.00 \begin {gather*} \frac {x}{b^{2} x^{2} - 2 \, a b x + a^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 11, normalized size = 1.10 \begin {gather*} \frac {x}{{\left (b x - a\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 29, normalized size = 2.90 \begin {gather*} \frac {a}{\left (b x -a \right )^{2} b}+\frac {1}{\left (b x -a \right ) b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 20, normalized size = 2.00 \begin {gather*} \frac {x}{b^{2} x^{2} - 2 \, a b x + a^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.40, size = 10, normalized size = 1.00 \begin {gather*} \frac {x}{{\left (a-b\,x\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.25, size = 17, normalized size = 1.70 \begin {gather*} \frac {x}{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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