Optimal. Leaf size=119 \[ -\frac {a^{10}}{4 x^4}-\frac {10 a^9 b}{3 x^3}-\frac {45 a^8 b^2}{2 x^2}-\frac {120 a^7 b^3}{x}+210 a^6 b^4 \log (x)+252 a^5 b^5 x+105 a^4 b^6 x^2+40 a^3 b^7 x^3+\frac {45}{4} a^2 b^8 x^4+2 a b^9 x^5+\frac {b^{10} x^6}{6} \]
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Rubi [A] time = 0.05, antiderivative size = 119, 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} \[ -\frac {45 a^8 b^2}{2 x^2}+105 a^4 b^6 x^2+40 a^3 b^7 x^3+\frac {45}{4} a^2 b^8 x^4-\frac {120 a^7 b^3}{x}+252 a^5 b^5 x+210 a^6 b^4 \log (x)-\frac {10 a^9 b}{3 x^3}-\frac {a^{10}}{4 x^4}+2 a b^9 x^5+\frac {b^{10} x^6}{6} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^{10}}{x^5} \, dx &=\int \left (252 a^5 b^5+\frac {a^{10}}{x^5}+\frac {10 a^9 b}{x^4}+\frac {45 a^8 b^2}{x^3}+\frac {120 a^7 b^3}{x^2}+\frac {210 a^6 b^4}{x}+210 a^4 b^6 x+120 a^3 b^7 x^2+45 a^2 b^8 x^3+10 a b^9 x^4+b^{10} x^5\right ) \, dx\\ &=-\frac {a^{10}}{4 x^4}-\frac {10 a^9 b}{3 x^3}-\frac {45 a^8 b^2}{2 x^2}-\frac {120 a^7 b^3}{x}+252 a^5 b^5 x+105 a^4 b^6 x^2+40 a^3 b^7 x^3+\frac {45}{4} a^2 b^8 x^4+2 a b^9 x^5+\frac {b^{10} x^6}{6}+210 a^6 b^4 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 119, normalized size = 1.00 \[ -\frac {a^{10}}{4 x^4}-\frac {10 a^9 b}{3 x^3}-\frac {45 a^8 b^2}{2 x^2}-\frac {120 a^7 b^3}{x}+210 a^6 b^4 \log (x)+252 a^5 b^5 x+105 a^4 b^6 x^2+40 a^3 b^7 x^3+\frac {45}{4} a^2 b^8 x^4+2 a b^9 x^5+\frac {b^{10} x^6}{6} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 114, normalized size = 0.96 \[ \frac {2 \, b^{10} x^{10} + 24 \, a b^{9} x^{9} + 135 \, a^{2} b^{8} x^{8} + 480 \, a^{3} b^{7} x^{7} + 1260 \, a^{4} b^{6} x^{6} + 3024 \, a^{5} b^{5} x^{5} + 2520 \, a^{6} b^{4} x^{4} \log \relax (x) - 1440 \, a^{7} b^{3} x^{3} - 270 \, a^{8} b^{2} x^{2} - 40 \, a^{9} b x - 3 \, a^{10}}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.12, size = 111, normalized size = 0.93 \[ \frac {1}{6} \, b^{10} x^{6} + 2 \, a b^{9} x^{5} + \frac {45}{4} \, a^{2} b^{8} x^{4} + 40 \, a^{3} b^{7} x^{3} + 105 \, a^{4} b^{6} x^{2} + 252 \, a^{5} b^{5} x + 210 \, a^{6} b^{4} \log \left ({\left | x \right |}\right ) - \frac {1440 \, a^{7} b^{3} x^{3} + 270 \, a^{8} b^{2} x^{2} + 40 \, a^{9} b x + 3 \, a^{10}}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 110, normalized size = 0.92 \[ \frac {b^{10} x^{6}}{6}+2 a \,b^{9} x^{5}+\frac {45 a^{2} b^{8} x^{4}}{4}+40 a^{3} b^{7} x^{3}+105 a^{4} b^{6} x^{2}+210 a^{6} b^{4} \ln \relax (x )+252 a^{5} b^{5} x -\frac {120 a^{7} b^{3}}{x}-\frac {45 a^{8} b^{2}}{2 x^{2}}-\frac {10 a^{9} b}{3 x^{3}}-\frac {a^{10}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.27, size = 110, normalized size = 0.92 \[ \frac {1}{6} \, b^{10} x^{6} + 2 \, a b^{9} x^{5} + \frac {45}{4} \, a^{2} b^{8} x^{4} + 40 \, a^{3} b^{7} x^{3} + 105 \, a^{4} b^{6} x^{2} + 252 \, a^{5} b^{5} x + 210 \, a^{6} b^{4} \log \relax (x) - \frac {1440 \, a^{7} b^{3} x^{3} + 270 \, a^{8} b^{2} x^{2} + 40 \, a^{9} b x + 3 \, a^{10}}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 110, normalized size = 0.92 \[ \frac {b^{10}\,x^6}{6}-\frac {\frac {a^{10}}{4}+\frac {10\,a^9\,b\,x}{3}+\frac {45\,a^8\,b^2\,x^2}{2}+120\,a^7\,b^3\,x^3}{x^4}+252\,a^5\,b^5\,x+2\,a\,b^9\,x^5+105\,a^4\,b^6\,x^2+40\,a^3\,b^7\,x^3+\frac {45\,a^2\,b^8\,x^4}{4}+210\,a^6\,b^4\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.44, size = 121, normalized size = 1.02 \[ 210 a^{6} b^{4} \log {\relax (x )} + 252 a^{5} b^{5} x + 105 a^{4} b^{6} x^{2} + 40 a^{3} b^{7} x^{3} + \frac {45 a^{2} b^{8} x^{4}}{4} + 2 a b^{9} x^{5} + \frac {b^{10} x^{6}}{6} + \frac {- 3 a^{10} - 40 a^{9} b x - 270 a^{8} b^{2} x^{2} - 1440 a^{7} b^{3} x^{3}}{12 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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