Optimal. Leaf size=117 \[ -\frac {a^{10}}{5 x^5}-\frac {5 a^9 b}{2 x^4}-\frac {15 a^8 b^2}{x^3}-\frac {60 a^7 b^3}{x^2}-\frac {210 a^6 b^4}{x}+252 a^5 b^5 \log (x)+210 a^4 b^6 x+60 a^3 b^7 x^2+15 a^2 b^8 x^3+\frac {5}{2} a b^9 x^4+\frac {b^{10} x^5}{5} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.05, antiderivative size = 117, 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} \[ -\frac {15 a^8 b^2}{x^3}-\frac {60 a^7 b^3}{x^2}+60 a^3 b^7 x^2+15 a^2 b^8 x^3-\frac {210 a^6 b^4}{x}+210 a^4 b^6 x+252 a^5 b^5 \log (x)-\frac {5 a^9 b}{2 x^4}-\frac {a^{10}}{5 x^5}+\frac {5}{2} a b^9 x^4+\frac {b^{10} x^5}{5} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^{10}}{x^6} \, dx &=\int \left (210 a^4 b^6+\frac {a^{10}}{x^6}+\frac {10 a^9 b}{x^5}+\frac {45 a^8 b^2}{x^4}+\frac {120 a^7 b^3}{x^3}+\frac {210 a^6 b^4}{x^2}+\frac {252 a^5 b^5}{x}+120 a^3 b^7 x+45 a^2 b^8 x^2+10 a b^9 x^3+b^{10} x^4\right ) \, dx\\ &=-\frac {a^{10}}{5 x^5}-\frac {5 a^9 b}{2 x^4}-\frac {15 a^8 b^2}{x^3}-\frac {60 a^7 b^3}{x^2}-\frac {210 a^6 b^4}{x}+210 a^4 b^6 x+60 a^3 b^7 x^2+15 a^2 b^8 x^3+\frac {5}{2} a b^9 x^4+\frac {b^{10} x^5}{5}+252 a^5 b^5 \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 117, normalized size = 1.00 \[ -\frac {a^{10}}{5 x^5}-\frac {5 a^9 b}{2 x^4}-\frac {15 a^8 b^2}{x^3}-\frac {60 a^7 b^3}{x^2}-\frac {210 a^6 b^4}{x}+252 a^5 b^5 \log (x)+210 a^4 b^6 x+60 a^3 b^7 x^2+15 a^2 b^8 x^3+\frac {5}{2} a b^9 x^4+\frac {b^{10} x^5}{5} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.47, size = 114, normalized size = 0.97 \[ \frac {2 \, b^{10} x^{10} + 25 \, a b^{9} x^{9} + 150 \, a^{2} b^{8} x^{8} + 600 \, a^{3} b^{7} x^{7} + 2100 \, a^{4} b^{6} x^{6} + 2520 \, a^{5} b^{5} x^{5} \log \relax (x) - 2100 \, a^{6} b^{4} x^{4} - 600 \, a^{7} b^{3} x^{3} - 150 \, a^{8} b^{2} x^{2} - 25 \, a^{9} b x - 2 \, a^{10}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.14, size = 111, normalized size = 0.95 \[ \frac {1}{5} \, b^{10} x^{5} + \frac {5}{2} \, a b^{9} x^{4} + 15 \, a^{2} b^{8} x^{3} + 60 \, a^{3} b^{7} x^{2} + 210 \, a^{4} b^{6} x + 252 \, a^{5} b^{5} \log \left ({\left | x \right |}\right ) - \frac {2100 \, a^{6} b^{4} x^{4} + 600 \, a^{7} b^{3} x^{3} + 150 \, a^{8} b^{2} x^{2} + 25 \, a^{9} b x + 2 \, a^{10}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 110, normalized size = 0.94 \[ \frac {b^{10} x^{5}}{5}+\frac {5 a \,b^{9} x^{4}}{2}+15 a^{2} b^{8} x^{3}+60 a^{3} b^{7} x^{2}+252 a^{5} b^{5} \ln \relax (x )+210 a^{4} b^{6} x -\frac {210 a^{6} b^{4}}{x}-\frac {60 a^{7} b^{3}}{x^{2}}-\frac {15 a^{8} b^{2}}{x^{3}}-\frac {5 a^{9} b}{2 x^{4}}-\frac {a^{10}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.40, size = 110, normalized size = 0.94 \[ \frac {1}{5} \, b^{10} x^{5} + \frac {5}{2} \, a b^{9} x^{4} + 15 \, a^{2} b^{8} x^{3} + 60 \, a^{3} b^{7} x^{2} + 210 \, a^{4} b^{6} x + 252 \, a^{5} b^{5} \log \relax (x) - \frac {2100 \, a^{6} b^{4} x^{4} + 600 \, a^{7} b^{3} x^{3} + 150 \, a^{8} b^{2} x^{2} + 25 \, a^{9} b x + 2 \, a^{10}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.10, size = 110, normalized size = 0.94 \[ \frac {b^{10}\,x^5}{5}-\frac {\frac {a^{10}}{5}+\frac {5\,a^9\,b\,x}{2}+15\,a^8\,b^2\,x^2+60\,a^7\,b^3\,x^3+210\,a^6\,b^4\,x^4}{x^5}+210\,a^4\,b^6\,x+\frac {5\,a\,b^9\,x^4}{2}+60\,a^3\,b^7\,x^2+15\,a^2\,b^8\,x^3+252\,a^5\,b^5\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.57, size = 121, normalized size = 1.03 \[ 252 a^{5} b^{5} \log {\relax (x )} + 210 a^{4} b^{6} x + 60 a^{3} b^{7} x^{2} + 15 a^{2} b^{8} x^{3} + \frac {5 a b^{9} x^{4}}{2} + \frac {b^{10} x^{5}}{5} + \frac {- 2 a^{10} - 25 a^{9} b x - 150 a^{8} b^{2} x^{2} - 600 a^{7} b^{3} x^{3} - 2100 a^{6} b^{4} x^{4}}{10 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________