Optimal. Leaf size=87 \[ a^7 \log (x)+7 a^6 b x+\frac {21}{2} a^5 b^2 x^2+\frac {35}{3} a^4 b^3 x^3+\frac {35}{4} a^3 b^4 x^4+\frac {21}{5} a^2 b^5 x^5+\frac {7}{6} a b^6 x^6+\frac {b^7 x^7}{7} \]
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Rubi [A] time = 0.03, antiderivative size = 87, 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} \[ \frac {21}{2} a^5 b^2 x^2+\frac {35}{3} a^4 b^3 x^3+\frac {35}{4} a^3 b^4 x^4+\frac {21}{5} a^2 b^5 x^5+7 a^6 b x+a^7 \log (x)+\frac {7}{6} a b^6 x^6+\frac {b^7 x^7}{7} \]
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*}
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Mathematica [A] time = 0.00, size = 87, normalized size = 1.00 \[ a^7 \log (x)+7 a^6 b x+\frac {21}{2} a^5 b^2 x^2+\frac {35}{3} a^4 b^3 x^3+\frac {35}{4} a^3 b^4 x^4+\frac {21}{5} a^2 b^5 x^5+\frac {7}{6} a b^6 x^6+\frac {b^7 x^7}{7} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 75, normalized size = 0.86 \[ \frac {1}{7} \, b^{7} x^{7} + \frac {7}{6} \, a b^{6} x^{6} + \frac {21}{5} \, a^{2} b^{5} x^{5} + \frac {35}{4} \, a^{3} b^{4} x^{4} + \frac {35}{3} \, a^{4} b^{3} x^{3} + \frac {21}{2} \, a^{5} b^{2} x^{2} + 7 \, a^{6} b x + a^{7} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.30, size = 76, normalized size = 0.87 \[ \frac {1}{7} \, b^{7} x^{7} + \frac {7}{6} \, a b^{6} x^{6} + \frac {21}{5} \, a^{2} b^{5} x^{5} + \frac {35}{4} \, a^{3} b^{4} x^{4} + \frac {35}{3} \, a^{4} b^{3} x^{3} + \frac {21}{2} \, a^{5} b^{2} x^{2} + 7 \, a^{6} b x + a^{7} \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 76, normalized size = 0.87 \[ \frac {b^{7} x^{7}}{7}+\frac {7 a \,b^{6} x^{6}}{6}+\frac {21 a^{2} b^{5} x^{5}}{5}+\frac {35 a^{3} b^{4} x^{4}}{4}+\frac {35 a^{4} b^{3} x^{3}}{3}+\frac {21 a^{5} b^{2} x^{2}}{2}+a^{7} \ln \relax (x )+7 a^{6} b x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 75, normalized size = 0.86 \[ \frac {1}{7} \, b^{7} x^{7} + \frac {7}{6} \, a b^{6} x^{6} + \frac {21}{5} \, a^{2} b^{5} x^{5} + \frac {35}{4} \, a^{3} b^{4} x^{4} + \frac {35}{3} \, a^{4} b^{3} x^{3} + \frac {21}{2} \, a^{5} b^{2} x^{2} + 7 \, a^{6} b x + a^{7} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 75, normalized size = 0.86 \[ a^7\,\ln \relax (x)+\frac {b^7\,x^7}{7}+\frac {7\,a\,b^6\,x^6}{6}+\frac {21\,a^5\,b^2\,x^2}{2}+\frac {35\,a^4\,b^3\,x^3}{3}+\frac {35\,a^3\,b^4\,x^4}{4}+\frac {21\,a^2\,b^5\,x^5}{5}+7\,a^6\,b\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 88, normalized size = 1.01 \[ a^{7} \log {\relax (x )} + 7 a^{6} b x + \frac {21 a^{5} b^{2} x^{2}}{2} + \frac {35 a^{4} b^{3} x^{3}}{3} + \frac {35 a^{3} b^{4} x^{4}}{4} + \frac {21 a^{2} b^{5} x^{5}}{5} + \frac {7 a b^{6} x^{6}}{6} + \frac {b^{7} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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