Optimal. Leaf size=58 \[ -\frac {a^5}{x}+5 a^4 b \log (x)+10 a^3 b^2 x+5 a^2 b^3 x^2+\frac {5}{3} a b^4 x^3+\frac {b^5 x^4}{4} \]
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Rubi [A] time = 0.02, antiderivative size = 58, 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} \[ 5 a^2 b^3 x^2+10 a^3 b^2 x+5 a^4 b \log (x)-\frac {a^5}{x}+\frac {5}{3} a b^4 x^3+\frac {b^5 x^4}{4} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^5}{x^2} \, dx &=\int \left (10 a^3 b^2+\frac {a^5}{x^2}+\frac {5 a^4 b}{x}+10 a^2 b^3 x+5 a b^4 x^2+b^5 x^3\right ) \, dx\\ &=-\frac {a^5}{x}+10 a^3 b^2 x+5 a^2 b^3 x^2+\frac {5}{3} a b^4 x^3+\frac {b^5 x^4}{4}+5 a^4 b \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 58, normalized size = 1.00 \[ -\frac {a^5}{x}+5 a^4 b \log (x)+10 a^3 b^2 x+5 a^2 b^3 x^2+\frac {5}{3} a b^4 x^3+\frac {b^5 x^4}{4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 59, normalized size = 1.02 \[ \frac {3 \, b^{5} x^{5} + 20 \, a b^{4} x^{4} + 60 \, a^{2} b^{3} x^{3} + 120 \, a^{3} b^{2} x^{2} + 60 \, a^{4} b x \log \relax (x) - 12 \, a^{5}}{12 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.28, size = 55, normalized size = 0.95 \[ \frac {1}{4} \, b^{5} x^{4} + \frac {5}{3} \, a b^{4} x^{3} + 5 \, a^{2} b^{3} x^{2} + 10 \, a^{3} b^{2} x + 5 \, a^{4} b \log \left ({\left | x \right |}\right ) - \frac {a^{5}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 55, normalized size = 0.95 \[ \frac {b^{5} x^{4}}{4}+\frac {5 a \,b^{4} x^{3}}{3}+5 a^{2} b^{3} x^{2}+5 a^{4} b \ln \relax (x )+10 a^{3} b^{2} x -\frac {a^{5}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.40, size = 54, normalized size = 0.93 \[ \frac {1}{4} \, b^{5} x^{4} + \frac {5}{3} \, a b^{4} x^{3} + 5 \, a^{2} b^{3} x^{2} + 10 \, a^{3} b^{2} x + 5 \, a^{4} b \log \relax (x) - \frac {a^{5}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 54, normalized size = 0.93 \[ \frac {b^5\,x^4}{4}-\frac {a^5}{x}+10\,a^3\,b^2\,x+\frac {5\,a\,b^4\,x^3}{3}+5\,a^4\,b\,\ln \relax (x)+5\,a^2\,b^3\,x^2 \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 56, normalized size = 0.97 \[ - \frac {a^{5}}{x} + 5 a^{4} b \log {\relax (x )} + 10 a^{3} b^{2} x + 5 a^{2} b^{3} x^{2} + \frac {5 a b^{4} x^{3}}{3} + \frac {b^{5} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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