Optimal. Leaf size=10 \[ -\frac{1}{x (a+b)^2} \]
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Rubi [A] time = 0.0032584, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {6, 12, 30} \[ -\frac{1}{x (a+b)^2} \]
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{(a x+b x)^2} \, dx &=\int \frac{1}{(a+b)^2 x^2} \, dx\\ &=\frac{\int \frac{1}{x^2} \, dx}{(a+b)^2}\\ &=-\frac{1}{(a+b)^2 x}\\ \end{align*}
Mathematica [A] time = 0.0030123, size = 10, normalized size = 1. \[ -\frac{1}{x (a+b)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 11, normalized size = 1.1 \begin{align*} -{\frac{1}{ \left ( a+b \right ) ^{2}x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11015, size = 22, normalized size = 2.2 \begin{align*} -\frac{1}{{\left (a x + b x\right )}{\left (a + b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.800912, size = 38, normalized size = 3.8 \begin{align*} -\frac{1}{{\left (a^{2} + 2 \, a b + b^{2}\right )} x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.111881, size = 15, normalized size = 1.5 \begin{align*} - \frac{1}{x \left (a^{2} + 2 a b + b^{2}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12956, size = 22, normalized size = 2.2 \begin{align*} -\frac{1}{{\left (a x + b x\right )}{\left (a + b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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