Optimal. Leaf size=84 \[ -\frac {a^7}{5 x^5}-\frac {7 a^6 b}{4 x^4}-\frac {7 a^5 b^2}{x^3}-\frac {35 a^4 b^3}{2 x^2}-\frac {35 a^3 b^4}{x}+21 a^2 b^5 \log (x)+7 a b^6 x+\frac {b^7 x^2}{2} \]
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Rubi [A] time = 0.03, antiderivative size = 84, 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} \[ -\frac {7 a^5 b^2}{x^3}-\frac {35 a^4 b^3}{2 x^2}-\frac {35 a^3 b^4}{x}+21 a^2 b^5 \log (x)-\frac {7 a^6 b}{4 x^4}-\frac {a^7}{5 x^5}+7 a b^6 x+\frac {b^7 x^2}{2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^7}{x^6} \, dx &=\int \left (7 a b^6+\frac {a^7}{x^6}+\frac {7 a^6 b}{x^5}+\frac {21 a^5 b^2}{x^4}+\frac {35 a^4 b^3}{x^3}+\frac {35 a^3 b^4}{x^2}+\frac {21 a^2 b^5}{x}+b^7 x\right ) \, dx\\ &=-\frac {a^7}{5 x^5}-\frac {7 a^6 b}{4 x^4}-\frac {7 a^5 b^2}{x^3}-\frac {35 a^4 b^3}{2 x^2}-\frac {35 a^3 b^4}{x}+7 a b^6 x+\frac {b^7 x^2}{2}+21 a^2 b^5 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 84, normalized size = 1.00 \[ -\frac {a^7}{5 x^5}-\frac {7 a^6 b}{4 x^4}-\frac {7 a^5 b^2}{x^3}-\frac {35 a^4 b^3}{2 x^2}-\frac {35 a^3 b^4}{x}+21 a^2 b^5 \log (x)+7 a b^6 x+\frac {b^7 x^2}{2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 81, normalized size = 0.96 \[ \frac {10 \, b^{7} x^{7} + 140 \, a b^{6} x^{6} + 420 \, a^{2} b^{5} x^{5} \log \relax (x) - 700 \, a^{3} b^{4} x^{4} - 350 \, a^{4} b^{3} x^{3} - 140 \, a^{5} b^{2} x^{2} - 35 \, a^{6} b x - 4 \, a^{7}}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.01, size = 78, normalized size = 0.93 \[ \frac {1}{2} \, b^{7} x^{2} + 7 \, a b^{6} x + 21 \, a^{2} b^{5} \log \left ({\left | x \right |}\right ) - \frac {700 \, a^{3} b^{4} x^{4} + 350 \, a^{4} b^{3} x^{3} + 140 \, a^{5} b^{2} x^{2} + 35 \, a^{6} b x + 4 \, a^{7}}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 77, normalized size = 0.92 \[ \frac {b^{7} x^{2}}{2}+21 a^{2} b^{5} \ln \relax (x )+7 a \,b^{6} x -\frac {35 a^{3} b^{4}}{x}-\frac {35 a^{4} b^{3}}{2 x^{2}}-\frac {7 a^{5} b^{2}}{x^{3}}-\frac {7 a^{6} b}{4 x^{4}}-\frac {a^{7}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.38, size = 77, normalized size = 0.92 \[ \frac {1}{2} \, b^{7} x^{2} + 7 \, a b^{6} x + 21 \, a^{2} b^{5} \log \relax (x) - \frac {700 \, a^{3} b^{4} x^{4} + 350 \, a^{4} b^{3} x^{3} + 140 \, a^{5} b^{2} x^{2} + 35 \, a^{6} b x + 4 \, a^{7}}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 77, normalized size = 0.92 \[ \frac {b^7\,x^2}{2}-\frac {\frac {a^7}{5}+\frac {7\,a^6\,b\,x}{4}+7\,a^5\,b^2\,x^2+\frac {35\,a^4\,b^3\,x^3}{2}+35\,a^3\,b^4\,x^4}{x^5}+21\,a^2\,b^5\,\ln \relax (x)+7\,a\,b^6\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.45, size = 83, normalized size = 0.99 \[ 21 a^{2} b^{5} \log {\relax (x )} + 7 a b^{6} x + \frac {b^{7} x^{2}}{2} + \frac {- 4 a^{7} - 35 a^{6} b x - 140 a^{5} b^{2} x^{2} - 350 a^{4} b^{3} x^{3} - 700 a^{3} b^{4} x^{4}}{20 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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