Optimal. Leaf size=115 \[ -\frac{9 a^8 b^2}{x^5}-\frac{30 a^7 b^3}{x^4}-\frac{70 a^6 b^4}{x^3}-\frac{126 a^5 b^5}{x^2}-\frac{210 a^4 b^6}{x}+45 a^2 b^8 x+120 a^3 b^7 \log (x)-\frac{5 a^9 b}{3 x^6}-\frac{a^{10}}{7 x^7}+5 a b^9 x^2+\frac{b^{10} x^3}{3} \]
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Rubi [A] time = 0.0496511, antiderivative size = 115, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ -\frac{9 a^8 b^2}{x^5}-\frac{30 a^7 b^3}{x^4}-\frac{70 a^6 b^4}{x^3}-\frac{126 a^5 b^5}{x^2}-\frac{210 a^4 b^6}{x}+45 a^2 b^8 x+120 a^3 b^7 \log (x)-\frac{5 a^9 b}{3 x^6}-\frac{a^{10}}{7 x^7}+5 a b^9 x^2+\frac{b^{10} x^3}{3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^{10}}{x^8} \, dx &=\int \left (45 a^2 b^8+\frac{a^{10}}{x^8}+\frac{10 a^9 b}{x^7}+\frac{45 a^8 b^2}{x^6}+\frac{120 a^7 b^3}{x^5}+\frac{210 a^6 b^4}{x^4}+\frac{252 a^5 b^5}{x^3}+\frac{210 a^4 b^6}{x^2}+\frac{120 a^3 b^7}{x}+10 a b^9 x+b^{10} x^2\right ) \, dx\\ &=-\frac{a^{10}}{7 x^7}-\frac{5 a^9 b}{3 x^6}-\frac{9 a^8 b^2}{x^5}-\frac{30 a^7 b^3}{x^4}-\frac{70 a^6 b^4}{x^3}-\frac{126 a^5 b^5}{x^2}-\frac{210 a^4 b^6}{x}+45 a^2 b^8 x+5 a b^9 x^2+\frac{b^{10} x^3}{3}+120 a^3 b^7 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0159778, size = 115, normalized size = 1. \[ -\frac{9 a^8 b^2}{x^5}-\frac{30 a^7 b^3}{x^4}-\frac{70 a^6 b^4}{x^3}-\frac{126 a^5 b^5}{x^2}-\frac{210 a^4 b^6}{x}+45 a^2 b^8 x+120 a^3 b^7 \log (x)-\frac{5 a^9 b}{3 x^6}-\frac{a^{10}}{7 x^7}+5 a b^9 x^2+\frac{b^{10} x^3}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 110, normalized size = 1. \begin{align*} -{\frac{{a}^{10}}{7\,{x}^{7}}}-{\frac{5\,{a}^{9}b}{3\,{x}^{6}}}-9\,{\frac{{a}^{8}{b}^{2}}{{x}^{5}}}-30\,{\frac{{a}^{7}{b}^{3}}{{x}^{4}}}-70\,{\frac{{a}^{6}{b}^{4}}{{x}^{3}}}-126\,{\frac{{a}^{5}{b}^{5}}{{x}^{2}}}-210\,{\frac{{a}^{4}{b}^{6}}{x}}+45\,{a}^{2}{b}^{8}x+5\,a{b}^{9}{x}^{2}+{\frac{{b}^{10}{x}^{3}}{3}}+120\,{a}^{3}{b}^{7}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05544, size = 149, normalized size = 1.3 \begin{align*} \frac{1}{3} \, b^{10} x^{3} + 5 \, a b^{9} x^{2} + 45 \, a^{2} b^{8} x + 120 \, a^{3} b^{7} \log \left (x\right ) - \frac{4410 \, a^{4} b^{6} x^{6} + 2646 \, a^{5} b^{5} x^{5} + 1470 \, a^{6} b^{4} x^{4} + 630 \, a^{7} b^{3} x^{3} + 189 \, a^{8} b^{2} x^{2} + 35 \, a^{9} b x + 3 \, a^{10}}{21 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.59277, size = 269, normalized size = 2.34 \begin{align*} \frac{7 \, b^{10} x^{10} + 105 \, a b^{9} x^{9} + 945 \, a^{2} b^{8} x^{8} + 2520 \, a^{3} b^{7} x^{7} \log \left (x\right ) - 4410 \, a^{4} b^{6} x^{6} - 2646 \, a^{5} b^{5} x^{5} - 1470 \, a^{6} b^{4} x^{4} - 630 \, a^{7} b^{3} x^{3} - 189 \, a^{8} b^{2} x^{2} - 35 \, a^{9} b x - 3 \, a^{10}}{21 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.99561, size = 117, normalized size = 1.02 \begin{align*} 120 a^{3} b^{7} \log{\left (x \right )} + 45 a^{2} b^{8} x + 5 a b^{9} x^{2} + \frac{b^{10} x^{3}}{3} - \frac{3 a^{10} + 35 a^{9} b x + 189 a^{8} b^{2} x^{2} + 630 a^{7} b^{3} x^{3} + 1470 a^{6} b^{4} x^{4} + 2646 a^{5} b^{5} x^{5} + 4410 a^{4} b^{6} x^{6}}{21 x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.23328, size = 150, normalized size = 1.3 \begin{align*} \frac{1}{3} \, b^{10} x^{3} + 5 \, a b^{9} x^{2} + 45 \, a^{2} b^{8} x + 120 \, a^{3} b^{7} \log \left ({\left | x \right |}\right ) - \frac{4410 \, a^{4} b^{6} x^{6} + 2646 \, a^{5} b^{5} x^{5} + 1470 \, a^{6} b^{4} x^{4} + 630 \, a^{7} b^{3} x^{3} + 189 \, a^{8} b^{2} x^{2} + 35 \, a^{9} b x + 3 \, a^{10}}{21 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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