Optimal. Leaf size=87 \[ \frac{21}{2} a^5 b^2 x^2+\frac{35}{3} a^4 b^3 x^3+\frac{35}{4} a^3 b^4 x^4+\frac{21}{5} a^2 b^5 x^5+7 a^6 b x+a^7 \log (x)+\frac{7}{6} a b^6 x^6+\frac{b^7 x^7}{7} \]
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Rubi [A] time = 0.0273506, antiderivative size = 87, 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} \[ \frac{21}{2} a^5 b^2 x^2+\frac{35}{3} a^4 b^3 x^3+\frac{35}{4} a^3 b^4 x^4+\frac{21}{5} a^2 b^5 x^5+7 a^6 b x+a^7 \log (x)+\frac{7}{6} a b^6 x^6+\frac{b^7 x^7}{7} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^7}{x} \, dx &=\int \left (7 a^6 b+\frac{a^7}{x}+21 a^5 b^2 x+35 a^4 b^3 x^2+35 a^3 b^4 x^3+21 a^2 b^5 x^4+7 a b^6 x^5+b^7 x^6\right ) \, dx\\ &=7 a^6 b x+\frac{21}{2} a^5 b^2 x^2+\frac{35}{3} a^4 b^3 x^3+\frac{35}{4} a^3 b^4 x^4+\frac{21}{5} a^2 b^5 x^5+\frac{7}{6} a b^6 x^6+\frac{b^7 x^7}{7}+a^7 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0040599, size = 87, normalized size = 1. \[ \frac{21}{2} a^5 b^2 x^2+\frac{35}{3} a^4 b^3 x^3+\frac{35}{4} a^3 b^4 x^4+\frac{21}{5} a^2 b^5 x^5+7 a^6 b x+a^7 \log (x)+\frac{7}{6} a b^6 x^6+\frac{b^7 x^7}{7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 76, normalized size = 0.9 \begin{align*} 7\,{a}^{6}bx+{\frac{21\,{a}^{5}{b}^{2}{x}^{2}}{2}}+{\frac{35\,{a}^{4}{b}^{3}{x}^{3}}{3}}+{\frac{35\,{a}^{3}{b}^{4}{x}^{4}}{4}}+{\frac{21\,{a}^{2}{b}^{5}{x}^{5}}{5}}+{\frac{7\,a{b}^{6}{x}^{6}}{6}}+{\frac{{b}^{7}{x}^{7}}{7}}+{a}^{7}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03238, size = 101, normalized size = 1.16 \begin{align*} \frac{1}{7} \, b^{7} x^{7} + \frac{7}{6} \, a b^{6} x^{6} + \frac{21}{5} \, a^{2} b^{5} x^{5} + \frac{35}{4} \, a^{3} b^{4} x^{4} + \frac{35}{3} \, a^{4} b^{3} x^{3} + \frac{21}{2} \, a^{5} b^{2} x^{2} + 7 \, a^{6} b x + a^{7} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49098, size = 176, normalized size = 2.02 \begin{align*} \frac{1}{7} \, b^{7} x^{7} + \frac{7}{6} \, a b^{6} x^{6} + \frac{21}{5} \, a^{2} b^{5} x^{5} + \frac{35}{4} \, a^{3} b^{4} x^{4} + \frac{35}{3} \, a^{4} b^{3} x^{3} + \frac{21}{2} \, a^{5} b^{2} x^{2} + 7 \, a^{6} b x + a^{7} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.352165, size = 88, normalized size = 1.01 \begin{align*} a^{7} \log{\left (x \right )} + 7 a^{6} b x + \frac{21 a^{5} b^{2} x^{2}}{2} + \frac{35 a^{4} b^{3} x^{3}}{3} + \frac{35 a^{3} b^{4} x^{4}}{4} + \frac{21 a^{2} b^{5} x^{5}}{5} + \frac{7 a b^{6} x^{6}}{6} + \frac{b^{7} x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19813, size = 103, normalized size = 1.18 \begin{align*} \frac{1}{7} \, b^{7} x^{7} + \frac{7}{6} \, a b^{6} x^{6} + \frac{21}{5} \, a^{2} b^{5} x^{5} + \frac{35}{4} \, a^{3} b^{4} x^{4} + \frac{35}{3} \, a^{4} b^{3} x^{3} + \frac{21}{2} \, a^{5} b^{2} x^{2} + 7 \, a^{6} b x + a^{7} \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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