Optimal. Leaf size=85 \[ -\frac{21 a^5 b^2}{4 x^4}-\frac{35 a^4 b^3}{3 x^3}-\frac{35 a^3 b^4}{2 x^2}-\frac{21 a^2 b^5}{x}-\frac{7 a^6 b}{5 x^5}-\frac{a^7}{6 x^6}+7 a b^6 \log (x)+b^7 x \]
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Rubi [A] time = 0.0313059, antiderivative size = 85, 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} \[ -\frac{21 a^5 b^2}{4 x^4}-\frac{35 a^4 b^3}{3 x^3}-\frac{35 a^3 b^4}{2 x^2}-\frac{21 a^2 b^5}{x}-\frac{7 a^6 b}{5 x^5}-\frac{a^7}{6 x^6}+7 a b^6 \log (x)+b^7 x \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^7}{x^7} \, dx &=\int \left (b^7+\frac{a^7}{x^7}+\frac{7 a^6 b}{x^6}+\frac{21 a^5 b^2}{x^5}+\frac{35 a^4 b^3}{x^4}+\frac{35 a^3 b^4}{x^3}+\frac{21 a^2 b^5}{x^2}+\frac{7 a b^6}{x}\right ) \, dx\\ &=-\frac{a^7}{6 x^6}-\frac{7 a^6 b}{5 x^5}-\frac{21 a^5 b^2}{4 x^4}-\frac{35 a^4 b^3}{3 x^3}-\frac{35 a^3 b^4}{2 x^2}-\frac{21 a^2 b^5}{x}+b^7 x+7 a b^6 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0094263, size = 85, normalized size = 1. \[ -\frac{21 a^5 b^2}{4 x^4}-\frac{35 a^4 b^3}{3 x^3}-\frac{35 a^3 b^4}{2 x^2}-\frac{21 a^2 b^5}{x}-\frac{7 a^6 b}{5 x^5}-\frac{a^7}{6 x^6}+7 a b^6 \log (x)+b^7 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 76, normalized size = 0.9 \begin{align*} -{\frac{{a}^{7}}{6\,{x}^{6}}}-{\frac{7\,{a}^{6}b}{5\,{x}^{5}}}-{\frac{21\,{a}^{5}{b}^{2}}{4\,{x}^{4}}}-{\frac{35\,{a}^{4}{b}^{3}}{3\,{x}^{3}}}-{\frac{35\,{a}^{3}{b}^{4}}{2\,{x}^{2}}}-21\,{\frac{{a}^{2}{b}^{5}}{x}}+{b}^{7}x+7\,a{b}^{6}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01042, size = 103, normalized size = 1.21 \begin{align*} b^{7} x + 7 \, a b^{6} \log \left (x\right ) - \frac{1260 \, a^{2} b^{5} x^{5} + 1050 \, a^{3} b^{4} x^{4} + 700 \, a^{4} b^{3} x^{3} + 315 \, a^{5} b^{2} x^{2} + 84 \, a^{6} b x + 10 \, a^{7}}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.70654, size = 192, normalized size = 2.26 \begin{align*} \frac{60 \, b^{7} x^{7} + 420 \, a b^{6} x^{6} \log \left (x\right ) - 1260 \, a^{2} b^{5} x^{5} - 1050 \, a^{3} b^{4} x^{4} - 700 \, a^{4} b^{3} x^{3} - 315 \, a^{5} b^{2} x^{2} - 84 \, a^{6} b x - 10 \, a^{7}}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.734266, size = 80, normalized size = 0.94 \begin{align*} 7 a b^{6} \log{\left (x \right )} + b^{7} x - \frac{10 a^{7} + 84 a^{6} b x + 315 a^{5} b^{2} x^{2} + 700 a^{4} b^{3} x^{3} + 1050 a^{3} b^{4} x^{4} + 1260 a^{2} b^{5} x^{5}}{60 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16218, size = 104, normalized size = 1.22 \begin{align*} b^{7} x + 7 \, a b^{6} \log \left ({\left | x \right |}\right ) - \frac{1260 \, a^{2} b^{5} x^{5} + 1050 \, a^{3} b^{4} x^{4} + 700 \, a^{4} b^{3} x^{3} + 315 \, a^{5} b^{2} x^{2} + 84 \, a^{6} b x + 10 \, a^{7}}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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