Optimal. Leaf size=64 \[ -\frac {a^3 A}{3 x^3}-\frac {a^2 (a B+3 A b)}{2 x^2}+b^2 \log (x) (3 a B+A b)-\frac {3 a b (a B+A b)}{x}+b^3 B x \]
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Rubi [A] time = 0.04, antiderivative size = 64, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {76} \begin {gather*} -\frac {a^2 (a B+3 A b)}{2 x^2}-\frac {a^3 A}{3 x^3}+b^2 \log (x) (3 a B+A b)-\frac {3 a b (a B+A b)}{x}+b^3 B x \end {gather*}
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin {align*} \int \frac {(a+b x)^3 (A+B x)}{x^4} \, dx &=\int \left (b^3 B+\frac {a^3 A}{x^4}+\frac {a^2 (3 A b+a B)}{x^3}+\frac {3 a b (A b+a B)}{x^2}+\frac {b^2 (A b+3 a B)}{x}\right ) \, dx\\ &=-\frac {a^3 A}{3 x^3}-\frac {a^2 (3 A b+a B)}{2 x^2}-\frac {3 a b (A b+a B)}{x}+b^3 B x+b^2 (A b+3 a B) \log (x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 67, normalized size = 1.05 \begin {gather*} b^2 \log (x) (3 a B+A b)-\frac {a^3 (2 A+3 B x)+9 a^2 b x (A+2 B x)+18 a A b^2 x^2-6 b^3 B x^4}{6 x^3} \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)^3 (A+B x)}{x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.26, size = 75, normalized size = 1.17 \begin {gather*} \frac {6 \, B b^{3} x^{4} + 6 \, {\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} \log \relax (x) - 2 \, A a^{3} - 18 \, {\left (B a^{2} b + A a b^{2}\right )} x^{2} - 3 \, {\left (B a^{3} + 3 \, A a^{2} b\right )} x}{6 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.26, size = 70, normalized size = 1.09 \begin {gather*} B b^{3} x + {\left (3 \, B a b^{2} + A b^{3}\right )} \log \left ({\left | x \right |}\right ) - \frac {2 \, A a^{3} + 18 \, {\left (B a^{2} b + A a b^{2}\right )} x^{2} + 3 \, {\left (B a^{3} + 3 \, A a^{2} b\right )} x}{6 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 72, normalized size = 1.12 \begin {gather*} A \,b^{3} \ln \relax (x )+3 B a \,b^{2} \ln \relax (x )+B \,b^{3} x -\frac {3 A a \,b^{2}}{x}-\frac {3 B \,a^{2} b}{x}-\frac {3 A \,a^{2} b}{2 x^{2}}-\frac {B \,a^{3}}{2 x^{2}}-\frac {A \,a^{3}}{3 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.06, size = 69, normalized size = 1.08 \begin {gather*} B b^{3} x + {\left (3 \, B a b^{2} + A b^{3}\right )} \log \relax (x) - \frac {2 \, A a^{3} + 18 \, {\left (B a^{2} b + A a b^{2}\right )} x^{2} + 3 \, {\left (B a^{3} + 3 \, A a^{2} b\right )} x}{6 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.33, size = 70, normalized size = 1.09 \begin {gather*} \ln \relax (x)\,\left (A\,b^3+3\,B\,a\,b^2\right )-\frac {x^2\,\left (3\,B\,a^2\,b+3\,A\,a\,b^2\right )+x\,\left (\frac {B\,a^3}{2}+\frac {3\,A\,b\,a^2}{2}\right )+\frac {A\,a^3}{3}}{x^3}+B\,b^3\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.81, size = 73, normalized size = 1.14 \begin {gather*} B b^{3} x + b^{2} \left (A b + 3 B a\right ) \log {\relax (x )} + \frac {- 2 A a^{3} + x^{2} \left (- 18 A a b^{2} - 18 B a^{2} b\right ) + x \left (- 9 A a^{2} b - 3 B a^{3}\right )}{6 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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