Optimal. Leaf size=12 \[ \frac {1}{b (a-b x)} \]
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Rubi [A] time = 0.01, antiderivative size = 12, 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, 32} \begin {gather*} \frac {1}{b (a-b x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rule 627
Rubi steps
\begin {align*} \int \frac {(a+b x)^2}{\left (a^2-b^2 x^2\right )^2} \, dx &=\int \frac {1}{(a-b x)^2} \, dx\\ &=\frac {1}{b (a-b x)}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} \frac {1}{b (a-b x)} \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)^2}{\left (a^2-b^2 x^2\right )^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 14, normalized size = 1.17 \begin {gather*} -\frac {1}{b^{2} x - a b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 14, normalized size = 1.17 \begin {gather*} -\frac {1}{{\left (b x - a\right )} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 15, normalized size = 1.25 \begin {gather*} -\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 = 1.33, size = 14, normalized size = 1.17 \begin {gather*} -\frac {1}{b^{2} x - a b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.41, size = 12, normalized size = 1.00 \begin {gather*} \frac {1}{b\,\left (a-b\,x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 10, normalized size = 0.83 \begin {gather*} - \frac {1}{- a b + b^{2} x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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