Optimal. Leaf size=85 \[ -\frac {a^7}{6 x^6}-\frac {7 a^6 b}{5 x^5}-\frac {21 a^5 b^2}{4 x^4}-\frac {35 a^4 b^3}{3 x^3}-\frac {35 a^3 b^4}{2 x^2}-\frac {21 a^2 b^5}{x}+7 a b^6 \log (x)+b^7 x \]
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Rubi [A] time = 0.03, antiderivative size = 85, normalized size of antiderivative = 1.00, 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} \begin {gather*} -\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 \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 85, normalized size = 1.00 \begin {gather*} -\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}+7 a b^6 \log (x)+b^7 x \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+b x)^7}{x^7} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.40, size = 81, normalized size = 0.95 \begin {gather*} \frac {60 \, b^{7} x^{7} + 420 \, a b^{6} x^{6} \log \relax (x) - 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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.99, size = 77, normalized size = 0.91 \begin {gather*} 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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 76, normalized size = 0.89 \begin {gather*} 7 a \,b^{6} \ln \relax (x )+b^{7} x -\frac {21 a^{2} b^{5}}{x}-\frac {35 a^{3} b^{4}}{2 x^{2}}-\frac {35 a^{4} b^{3}}{3 x^{3}}-\frac {21 a^{5} b^{2}}{4 x^{4}}-\frac {7 a^{6} b}{5 x^{5}}-\frac {a^{7}}{6 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.38, size = 76, normalized size = 0.89 \begin {gather*} b^{7} x + 7 \, a b^{6} \log \relax (x) - \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 81, normalized size = 0.95 \begin {gather*} -\frac {10\,a^7-60\,b^7\,x^7+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+84\,a^6\,b\,x-420\,a\,b^6\,x^6\,\ln \relax (x)}{60\,x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.60, size = 82, normalized size = 0.96 \begin {gather*} 7 a b^{6} \log {\relax (x )} + 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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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