Optimal. Leaf size=114 \[ -\frac{45 a^8 b^2}{7 x^7}-\frac{20 a^7 b^3}{x^6}-\frac{42 a^6 b^4}{x^5}-\frac{63 a^5 b^5}{x^4}-\frac{70 a^4 b^6}{x^3}-\frac{60 a^3 b^7}{x^2}-\frac{45 a^2 b^8}{x}-\frac{5 a^9 b}{4 x^8}-\frac{a^{10}}{9 x^9}+10 a b^9 \log (x)+b^{10} x \]
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Rubi [A] time = 0.0530741, antiderivative size = 114, 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} \[ -\frac{45 a^8 b^2}{7 x^7}-\frac{20 a^7 b^3}{x^6}-\frac{42 a^6 b^4}{x^5}-\frac{63 a^5 b^5}{x^4}-\frac{70 a^4 b^6}{x^3}-\frac{60 a^3 b^7}{x^2}-\frac{45 a^2 b^8}{x}-\frac{5 a^9 b}{4 x^8}-\frac{a^{10}}{9 x^9}+10 a b^9 \log (x)+b^{10} x \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^{10}}{x^{10}} \, dx &=\int \left (b^{10}+\frac{a^{10}}{x^{10}}+\frac{10 a^9 b}{x^9}+\frac{45 a^8 b^2}{x^8}+\frac{120 a^7 b^3}{x^7}+\frac{210 a^6 b^4}{x^6}+\frac{252 a^5 b^5}{x^5}+\frac{210 a^4 b^6}{x^4}+\frac{120 a^3 b^7}{x^3}+\frac{45 a^2 b^8}{x^2}+\frac{10 a b^9}{x}\right ) \, dx\\ &=-\frac{a^{10}}{9 x^9}-\frac{5 a^9 b}{4 x^8}-\frac{45 a^8 b^2}{7 x^7}-\frac{20 a^7 b^3}{x^6}-\frac{42 a^6 b^4}{x^5}-\frac{63 a^5 b^5}{x^4}-\frac{70 a^4 b^6}{x^3}-\frac{60 a^3 b^7}{x^2}-\frac{45 a^2 b^8}{x}+b^{10} x+10 a b^9 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0077861, size = 114, normalized size = 1. \[ -\frac{45 a^8 b^2}{7 x^7}-\frac{20 a^7 b^3}{x^6}-\frac{42 a^6 b^4}{x^5}-\frac{63 a^5 b^5}{x^4}-\frac{70 a^4 b^6}{x^3}-\frac{60 a^3 b^7}{x^2}-\frac{45 a^2 b^8}{x}-\frac{5 a^9 b}{4 x^8}-\frac{a^{10}}{9 x^9}+10 a b^9 \log (x)+b^{10} x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 109, normalized size = 1. \begin{align*} -{\frac{{a}^{10}}{9\,{x}^{9}}}-{\frac{5\,{a}^{9}b}{4\,{x}^{8}}}-{\frac{45\,{a}^{8}{b}^{2}}{7\,{x}^{7}}}-20\,{\frac{{a}^{7}{b}^{3}}{{x}^{6}}}-42\,{\frac{{a}^{6}{b}^{4}}{{x}^{5}}}-63\,{\frac{{a}^{5}{b}^{5}}{{x}^{4}}}-70\,{\frac{{a}^{4}{b}^{6}}{{x}^{3}}}-60\,{\frac{{a}^{3}{b}^{7}}{{x}^{2}}}-45\,{\frac{{a}^{2}{b}^{8}}{x}}+{b}^{10}x+10\,a{b}^{9}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03206, size = 147, normalized size = 1.29 \begin{align*} b^{10} x + 10 \, a b^{9} \log \left (x\right ) - \frac{11340 \, a^{2} b^{8} x^{8} + 15120 \, a^{3} b^{7} x^{7} + 17640 \, a^{4} b^{6} x^{6} + 15876 \, a^{5} b^{5} x^{5} + 10584 \, a^{6} b^{4} x^{4} + 5040 \, a^{7} b^{3} x^{3} + 1620 \, a^{8} b^{2} x^{2} + 315 \, a^{9} b x + 28 \, a^{10}}{252 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.9087, size = 288, normalized size = 2.53 \begin{align*} \frac{252 \, b^{10} x^{10} + 2520 \, a b^{9} x^{9} \log \left (x\right ) - 11340 \, a^{2} b^{8} x^{8} - 15120 \, a^{3} b^{7} x^{7} - 17640 \, a^{4} b^{6} x^{6} - 15876 \, a^{5} b^{5} x^{5} - 10584 \, a^{6} b^{4} x^{4} - 5040 \, a^{7} b^{3} x^{3} - 1620 \, a^{8} b^{2} x^{2} - 315 \, a^{9} b x - 28 \, a^{10}}{252 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.11039, size = 116, normalized size = 1.02 \begin{align*} 10 a b^{9} \log{\left (x \right )} + b^{10} x - \frac{28 a^{10} + 315 a^{9} b x + 1620 a^{8} b^{2} x^{2} + 5040 a^{7} b^{3} x^{3} + 10584 a^{6} b^{4} x^{4} + 15876 a^{5} b^{5} x^{5} + 17640 a^{4} b^{6} x^{6} + 15120 a^{3} b^{7} x^{7} + 11340 a^{2} b^{8} x^{8}}{252 x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.23941, size = 149, normalized size = 1.31 \begin{align*} b^{10} x + 10 \, a b^{9} \log \left ({\left | x \right |}\right ) - \frac{11340 \, a^{2} b^{8} x^{8} + 15120 \, a^{3} b^{7} x^{7} + 17640 \, a^{4} b^{6} x^{6} + 15876 \, a^{5} b^{5} x^{5} + 10584 \, a^{6} b^{4} x^{4} + 5040 \, a^{7} b^{3} x^{3} + 1620 \, a^{8} b^{2} x^{2} + 315 \, a^{9} b x + 28 \, a^{10}}{252 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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