Optimal. Leaf size=134 \[ \frac{b^7}{2 a^8 x^2}-\frac{b^6}{3 a^7 x^3}+\frac{b^5}{4 a^6 x^4}-\frac{b^4}{5 a^5 x^5}+\frac{b^3}{6 a^4 x^6}-\frac{b^2}{7 a^3 x^7}-\frac{b^8}{a^9 x}-\frac{b^9 \log (x)}{a^{10}}+\frac{b^9 \log (a+b x)}{a^{10}}+\frac{b}{8 a^2 x^8}-\frac{1}{9 a x^9} \]
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Rubi [A] time = 0.0608035, antiderivative size = 134, 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 = {44} \[ \frac{b^7}{2 a^8 x^2}-\frac{b^6}{3 a^7 x^3}+\frac{b^5}{4 a^6 x^4}-\frac{b^4}{5 a^5 x^5}+\frac{b^3}{6 a^4 x^6}-\frac{b^2}{7 a^3 x^7}-\frac{b^8}{a^9 x}-\frac{b^9 \log (x)}{a^{10}}+\frac{b^9 \log (a+b x)}{a^{10}}+\frac{b}{8 a^2 x^8}-\frac{1}{9 a x^9} \]
Antiderivative was successfully verified.
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Rule 44
Rubi steps
\begin{align*} \int \frac{1}{x^{10} (a+b x)} \, dx &=\int \left (\frac{1}{a x^{10}}-\frac{b}{a^2 x^9}+\frac{b^2}{a^3 x^8}-\frac{b^3}{a^4 x^7}+\frac{b^4}{a^5 x^6}-\frac{b^5}{a^6 x^5}+\frac{b^6}{a^7 x^4}-\frac{b^7}{a^8 x^3}+\frac{b^8}{a^9 x^2}-\frac{b^9}{a^{10} x}+\frac{b^{10}}{a^{10} (a+b x)}\right ) \, dx\\ &=-\frac{1}{9 a x^9}+\frac{b}{8 a^2 x^8}-\frac{b^2}{7 a^3 x^7}+\frac{b^3}{6 a^4 x^6}-\frac{b^4}{5 a^5 x^5}+\frac{b^5}{4 a^6 x^4}-\frac{b^6}{3 a^7 x^3}+\frac{b^7}{2 a^8 x^2}-\frac{b^8}{a^9 x}-\frac{b^9 \log (x)}{a^{10}}+\frac{b^9 \log (a+b x)}{a^{10}}\\ \end{align*}
Mathematica [A] time = 0.0060532, size = 134, normalized size = 1. \[ \frac{b^7}{2 a^8 x^2}-\frac{b^6}{3 a^7 x^3}+\frac{b^5}{4 a^6 x^4}-\frac{b^4}{5 a^5 x^5}+\frac{b^3}{6 a^4 x^6}-\frac{b^2}{7 a^3 x^7}-\frac{b^8}{a^9 x}-\frac{b^9 \log (x)}{a^{10}}+\frac{b^9 \log (a+b x)}{a^{10}}+\frac{b}{8 a^2 x^8}-\frac{1}{9 a x^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 119, normalized size = 0.9 \begin{align*} -{\frac{1}{9\,a{x}^{9}}}+{\frac{b}{8\,{a}^{2}{x}^{8}}}-{\frac{{b}^{2}}{7\,{a}^{3}{x}^{7}}}+{\frac{{b}^{3}}{6\,{a}^{4}{x}^{6}}}-{\frac{{b}^{4}}{5\,{a}^{5}{x}^{5}}}+{\frac{{b}^{5}}{4\,{a}^{6}{x}^{4}}}-{\frac{{b}^{6}}{3\,{a}^{7}{x}^{3}}}+{\frac{{b}^{7}}{2\,{a}^{8}{x}^{2}}}-{\frac{{b}^{8}}{{a}^{9}x}}-{\frac{{b}^{9}\ln \left ( x \right ) }{{a}^{10}}}+{\frac{{b}^{9}\ln \left ( bx+a \right ) }{{a}^{10}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0785, size = 158, normalized size = 1.18 \begin{align*} \frac{b^{9} \log \left (b x + a\right )}{a^{10}} - \frac{b^{9} \log \left (x\right )}{a^{10}} - \frac{2520 \, b^{8} x^{8} - 1260 \, a b^{7} x^{7} + 840 \, a^{2} b^{6} x^{6} - 630 \, a^{3} b^{5} x^{5} + 504 \, a^{4} b^{4} x^{4} - 420 \, a^{5} b^{3} x^{3} + 360 \, a^{6} b^{2} x^{2} - 315 \, a^{7} b x + 280 \, a^{8}}{2520 \, a^{9} x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.78598, size = 296, normalized size = 2.21 \begin{align*} \frac{2520 \, b^{9} x^{9} \log \left (b x + a\right ) - 2520 \, b^{9} x^{9} \log \left (x\right ) - 2520 \, a b^{8} x^{8} + 1260 \, a^{2} b^{7} x^{7} - 840 \, a^{3} b^{6} x^{6} + 630 \, a^{4} b^{5} x^{5} - 504 \, a^{5} b^{4} x^{4} + 420 \, a^{6} b^{3} x^{3} - 360 \, a^{7} b^{2} x^{2} + 315 \, a^{8} b x - 280 \, a^{9}}{2520 \, a^{10} x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.00563, size = 116, normalized size = 0.87 \begin{align*} - \frac{280 a^{8} - 315 a^{7} b x + 360 a^{6} b^{2} x^{2} - 420 a^{5} b^{3} x^{3} + 504 a^{4} b^{4} x^{4} - 630 a^{3} b^{5} x^{5} + 840 a^{2} b^{6} x^{6} - 1260 a b^{7} x^{7} + 2520 b^{8} x^{8}}{2520 a^{9} x^{9}} + \frac{b^{9} \left (- \log{\left (x \right )} + \log{\left (\frac{a}{b} + x \right )}\right )}{a^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19382, size = 165, normalized size = 1.23 \begin{align*} \frac{b^{9} \log \left ({\left | b x + a \right |}\right )}{a^{10}} - \frac{b^{9} \log \left ({\left | x \right |}\right )}{a^{10}} - \frac{2520 \, a b^{8} x^{8} - 1260 \, a^{2} b^{7} x^{7} + 840 \, a^{3} b^{6} x^{6} - 630 \, a^{4} b^{5} x^{5} + 504 \, a^{5} b^{4} x^{4} - 420 \, a^{6} b^{3} x^{3} + 360 \, a^{7} b^{2} x^{2} - 315 \, a^{8} b x + 280 \, a^{9}}{2520 \, a^{10} x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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