Optimal. Leaf size=65 \[ -\frac {a^5}{5 x^5}-\frac {5 a^4 b}{2 x^2}+10 a^3 b^2 x+\frac {5}{2} a^2 b^3 x^4+\frac {5}{7} a b^4 x^7+\frac {b^5 x^{10}}{10} \]
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Rubi [A] time = 0.02, antiderivative size = 65, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {270} \[ \frac {5}{2} a^2 b^3 x^4+10 a^3 b^2 x-\frac {5 a^4 b}{2 x^2}-\frac {a^5}{5 x^5}+\frac {5}{7} a b^4 x^7+\frac {b^5 x^{10}}{10} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5}{x^6} \, dx &=\int \left (10 a^3 b^2+\frac {a^5}{x^6}+\frac {5 a^4 b}{x^3}+10 a^2 b^3 x^3+5 a b^4 x^6+b^5 x^9\right ) \, dx\\ &=-\frac {a^5}{5 x^5}-\frac {5 a^4 b}{2 x^2}+10 a^3 b^2 x+\frac {5}{2} a^2 b^3 x^4+\frac {5}{7} a b^4 x^7+\frac {b^5 x^{10}}{10}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 65, normalized size = 1.00 \[ -\frac {a^5}{5 x^5}-\frac {5 a^4 b}{2 x^2}+10 a^3 b^2 x+\frac {5}{2} a^2 b^3 x^4+\frac {5}{7} a b^4 x^7+\frac {b^5 x^{10}}{10} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 59, normalized size = 0.91 \[ \frac {7 \, b^{5} x^{15} + 50 \, a b^{4} x^{12} + 175 \, a^{2} b^{3} x^{9} + 700 \, a^{3} b^{2} x^{6} - 175 \, a^{4} b x^{3} - 14 \, a^{5}}{70 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 58, normalized size = 0.89 \[ \frac {1}{10} \, b^{5} x^{10} + \frac {5}{7} \, a b^{4} x^{7} + \frac {5}{2} \, a^{2} b^{3} x^{4} + 10 \, a^{3} b^{2} x - \frac {25 \, a^{4} b x^{3} + 2 \, a^{5}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 56, normalized size = 0.86 \[ \frac {b^{5} x^{10}}{10}+\frac {5 a \,b^{4} x^{7}}{7}+\frac {5 a^{2} b^{3} x^{4}}{2}+10 a^{3} b^{2} x -\frac {5 a^{4} b}{2 x^{2}}-\frac {a^{5}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 58, normalized size = 0.89 \[ \frac {1}{10} \, b^{5} x^{10} + \frac {5}{7} \, a b^{4} x^{7} + \frac {5}{2} \, a^{2} b^{3} x^{4} + 10 \, a^{3} b^{2} x - \frac {25 \, a^{4} b x^{3} + 2 \, a^{5}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 58, normalized size = 0.89 \[ \frac {b^5\,x^{10}}{10}-\frac {\frac {a^5}{5}+\frac {5\,b\,a^4\,x^3}{2}}{x^5}+10\,a^3\,b^2\,x+\frac {5\,a\,b^4\,x^7}{7}+\frac {5\,a^2\,b^3\,x^4}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 65, normalized size = 1.00 \[ 10 a^{3} b^{2} x + \frac {5 a^{2} b^{3} x^{4}}{2} + \frac {5 a b^{4} x^{7}}{7} + \frac {b^{5} x^{10}}{10} + \frac {- 2 a^{5} - 25 a^{4} b x^{3}}{10 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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