Optimal. Leaf size=75 \[ -\frac {a^3 A}{6 x^6}-\frac {a^2 (a B+3 A b)}{5 x^5}-\frac {b^2 (3 a B+A b)}{3 x^3}-\frac {3 a b (a B+A b)}{4 x^4}-\frac {b^3 B}{2 x^2} \]
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Rubi [A] time = 0.03, antiderivative size = 75, 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)}{5 x^5}-\frac {a^3 A}{6 x^6}-\frac {b^2 (3 a B+A b)}{3 x^3}-\frac {3 a b (a B+A b)}{4 x^4}-\frac {b^3 B}{2 x^2} \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^7} \, dx &=\int \left (\frac {a^3 A}{x^7}+\frac {a^2 (3 A b+a B)}{x^6}+\frac {3 a b (A b+a B)}{x^5}+\frac {b^2 (A b+3 a B)}{x^4}+\frac {b^3 B}{x^3}\right ) \, dx\\ &=-\frac {a^3 A}{6 x^6}-\frac {a^2 (3 A b+a B)}{5 x^5}-\frac {3 a b (A b+a B)}{4 x^4}-\frac {b^2 (A b+3 a B)}{3 x^3}-\frac {b^3 B}{2 x^2}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 69, normalized size = 0.92 \begin {gather*} -\frac {2 a^3 (5 A+6 B x)+9 a^2 b x (4 A+5 B x)+15 a b^2 x^2 (3 A+4 B x)+10 b^3 x^3 (2 A+3 B x)}{60 x^6} \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^7} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.24, size = 73, normalized size = 0.97 \begin {gather*} -\frac {30 \, B b^{3} x^{4} + 10 \, A a^{3} + 20 \, {\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 45 \, {\left (B a^{2} b + A a b^{2}\right )} x^{2} + 12 \, {\left (B a^{3} + 3 \, A a^{2} b\right )} x}{60 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.25, size = 75, normalized size = 1.00 \begin {gather*} -\frac {30 \, B b^{3} x^{4} + 60 \, B a b^{2} x^{3} + 20 \, A b^{3} x^{3} + 45 \, B a^{2} b x^{2} + 45 \, A a b^{2} x^{2} + 12 \, B a^{3} x + 36 \, A a^{2} b x + 10 \, A a^{3}}{60 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 66, normalized size = 0.88 \begin {gather*} -\frac {B \,b^{3}}{2 x^{2}}-\frac {\left (A b +3 B a \right ) b^{2}}{3 x^{3}}-\frac {A \,a^{3}}{6 x^{6}}-\frac {3 \left (A b +B a \right ) a b}{4 x^{4}}-\frac {\left (3 A b +B a \right ) a^{2}}{5 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.14, size = 73, normalized size = 0.97 \begin {gather*} -\frac {30 \, B b^{3} x^{4} + 10 \, A a^{3} + 20 \, {\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 45 \, {\left (B a^{2} b + A a b^{2}\right )} x^{2} + 12 \, {\left (B a^{3} + 3 \, A a^{2} b\right )} x}{60 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 73, normalized size = 0.97 \begin {gather*} -\frac {x^2\,\left (\frac {3\,B\,a^2\,b}{4}+\frac {3\,A\,a\,b^2}{4}\right )+x\,\left (\frac {B\,a^3}{5}+\frac {3\,A\,b\,a^2}{5}\right )+\frac {A\,a^3}{6}+x^3\,\left (\frac {A\,b^3}{3}+B\,a\,b^2\right )+\frac {B\,b^3\,x^4}{2}}{x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.30, size = 82, normalized size = 1.09 \begin {gather*} \frac {- 10 A a^{3} - 30 B b^{3} x^{4} + x^{3} \left (- 20 A b^{3} - 60 B a b^{2}\right ) + x^{2} \left (- 45 A a b^{2} - 45 B a^{2} b\right ) + x \left (- 36 A a^{2} b - 12 B a^{3}\right )}{60 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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