Optimal. Leaf size=33 \[ -\frac{a B+A b}{3 x^3}-\frac{a A}{4 x^4}-\frac{b B}{2 x^2} \]
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Rubi [A] time = 0.0129332, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {76} \[ -\frac{a B+A b}{3 x^3}-\frac{a A}{4 x^4}-\frac{b B}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin{align*} \int \frac{(a+b x) (A+B x)}{x^5} \, dx &=\int \left (\frac{a A}{x^5}+\frac{A b+a B}{x^4}+\frac{b B}{x^3}\right ) \, dx\\ &=-\frac{a A}{4 x^4}-\frac{A b+a B}{3 x^3}-\frac{b B}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0077658, size = 29, normalized size = 0.88 \[ -\frac{3 a A+4 a B x+4 A b x+6 b B x^2}{12 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 28, normalized size = 0.9 \begin{align*} -{\frac{Ab+Ba}{3\,{x}^{3}}}-{\frac{Aa}{4\,{x}^{4}}}-{\frac{Bb}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02378, size = 36, normalized size = 1.09 \begin{align*} -\frac{6 \, B b x^{2} + 3 \, A a + 4 \,{\left (B a + A b\right )} x}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.8114, size = 66, normalized size = 2. \begin{align*} -\frac{6 \, B b x^{2} + 3 \, A a + 4 \,{\left (B a + A b\right )} x}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.533122, size = 31, normalized size = 0.94 \begin{align*} - \frac{3 A a + 6 B b x^{2} + x \left (4 A b + 4 B a\right )}{12 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18884, size = 36, normalized size = 1.09 \begin{align*} -\frac{6 \, B b x^{2} + 4 \, B a x + 4 \, A b x + 3 \, A a}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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