Optimal. Leaf size=85 \[ -\frac {a^7}{6 x^6}-\frac {7 a^6 b}{5 x^5}-\frac {21 a^5 b^2}{4 x^4}-\frac {35 a^4 b^3}{3 x^3}-\frac {35 a^3 b^4}{2 x^2}-\frac {21 a^2 b^5}{x}+b^7 x+7 a b^6 \log (x) \]
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Rubi [A]
time = 0.02, 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 = {45}
\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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Rule 45
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 = 0.00, 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}+b^7 x+7 a b^6 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 2.32, size = 80, normalized size = 0.94 \begin {gather*} \frac {-a^2 \left (10 a^5+84 a^4 b x+315 a^3 b^2 x^2+700 a^2 b^3 x^3+1050 a b^4 x^4+1260 b^5 x^5\right )+60 b^6 x^6 \left (7 a \text {Log}\left [x\right ]+b x\right )}{60 x^6} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 76, normalized size = 0.89
method | result | size |
default | \(-\frac {a^{7}}{6 x^{6}}-\frac {7 a^{6} b}{5 x^{5}}-\frac {21 a^{5} b^{2}}{4 x^{4}}-\frac {35 a^{4} b^{3}}{3 x^{3}}-\frac {35 a^{3} b^{4}}{2 x^{2}}-\frac {21 a^{2} b^{5}}{x}+b^{7} x +7 a \,b^{6} \ln \left (x \right )\) | \(76\) |
risch | \(b^{7} x +\frac {-21 a^{2} b^{5} x^{5}-\frac {35}{2} a^{3} b^{4} x^{4}-\frac {35}{3} a^{4} b^{3} x^{3}-\frac {21}{4} a^{5} b^{2} x^{2}-\frac {7}{5} a^{6} b x -\frac {1}{6} a^{7}}{x^{6}}+7 a \,b^{6} \ln \left (x \right )\) | \(76\) |
norman | \(\frac {b^{7} x^{7}-\frac {1}{6} a^{7}-21 a^{2} b^{5} x^{5}-\frac {35}{2} a^{3} b^{4} x^{4}-\frac {35}{3} a^{4} b^{3} x^{3}-\frac {21}{4} a^{5} b^{2} x^{2}-\frac {7}{5} a^{6} b x}{x^{6}}+7 a \,b^{6} \ln \left (x \right )\) | \(78\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 76, normalized size = 0.89 \begin {gather*} 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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 81, normalized size = 0.95 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.23, size = 82, normalized size = 0.96 \begin {gather*} 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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 86, normalized size = 1.01 \begin {gather*} x b^{7}+\frac {\frac {1}{60} \left (-1260 b^{5} a^{2} x^{5}-1050 b^{4} a^{3} x^{4}-700 b^{3} a^{4} x^{3}-315 b^{2} a^{5} x^{2}-84 b a^{6} x-10 a^{7}\right )}{x^{6}}+7 b^{6} a \ln \left |x\right | \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 \left (x\right )}{60\,x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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