Optimal. Leaf size=55 \[ -\frac {a^2 A}{6 x^6}-\frac {a (a B+2 A b)}{5 x^5}-\frac {b (2 a B+A b)}{4 x^4}-\frac {b^2 B}{3 x^3} \]
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Rubi [A] time = 0.02, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {27, 76} \[ -\frac {a^2 A}{6 x^6}-\frac {a (a B+2 A b)}{5 x^5}-\frac {b (2 a B+A b)}{4 x^4}-\frac {b^2 B}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 27
Rule 76
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (a^2+2 a b x+b^2 x^2\right )}{x^7} \, dx &=\int \frac {(a+b x)^2 (A+B x)}{x^7} \, dx\\ &=\int \left (\frac {a^2 A}{x^7}+\frac {a (2 A b+a B)}{x^6}+\frac {b (A b+2 a B)}{x^5}+\frac {b^2 B}{x^4}\right ) \, dx\\ &=-\frac {a^2 A}{6 x^6}-\frac {a (2 A b+a B)}{5 x^5}-\frac {b (A b+2 a B)}{4 x^4}-\frac {b^2 B}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 50, normalized size = 0.91 \[ -\frac {2 a^2 (5 A+6 B x)+6 a b x (4 A+5 B x)+5 b^2 x^2 (3 A+4 B x)}{60 x^6} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 51, normalized size = 0.93 \[ -\frac {20 \, B b^{2} x^{3} + 10 \, A a^{2} + 15 \, {\left (2 \, B a b + A b^{2}\right )} x^{2} + 12 \, {\left (B a^{2} + 2 \, A a b\right )} x}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 51, normalized size = 0.93 \[ -\frac {20 \, B b^{2} x^{3} + 30 \, B a b x^{2} + 15 \, A b^{2} x^{2} + 12 \, B a^{2} x + 24 \, A a b x + 10 \, A a^{2}}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 48, normalized size = 0.87 \[ -\frac {B \,b^{2}}{3 x^{3}}-\frac {A \,a^{2}}{6 x^{6}}-\frac {\left (A b +2 B a \right ) b}{4 x^{4}}-\frac {\left (2 A b +B a \right ) a}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 51, normalized size = 0.93 \[ -\frac {20 \, B b^{2} x^{3} + 10 \, A a^{2} + 15 \, {\left (2 \, B a b + A b^{2}\right )} x^{2} + 12 \, {\left (B a^{2} + 2 \, A a b\right )} x}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 51, normalized size = 0.93 \[ -\frac {x^2\,\left (\frac {A\,b^2}{4}+\frac {B\,a\,b}{2}\right )+\frac {A\,a^2}{6}+x\,\left (\frac {B\,a^2}{5}+\frac {2\,A\,b\,a}{5}\right )+\frac {B\,b^2\,x^3}{3}}{x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.01, size = 56, normalized size = 1.02 \[ \frac {- 10 A a^{2} - 20 B b^{2} x^{3} + x^{2} \left (- 15 A b^{2} - 30 B a b\right ) + x \left (- 24 A a b - 12 B a^{2}\right )}{60 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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