Integrand size = 11, antiderivative size = 69 \[ \int \frac {(a+b x)^5}{x^{11}} \, dx=-\frac {a^5}{10 x^{10}}-\frac {5 a^4 b}{9 x^9}-\frac {5 a^3 b^2}{4 x^8}-\frac {10 a^2 b^3}{7 x^7}-\frac {5 a b^4}{6 x^6}-\frac {b^5}{5 x^5} \]
[Out]
Time = 0.01 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45} \[ \int \frac {(a+b x)^5}{x^{11}} \, dx=-\frac {a^5}{10 x^{10}}-\frac {5 a^4 b}{9 x^9}-\frac {5 a^3 b^2}{4 x^8}-\frac {10 a^2 b^3}{7 x^7}-\frac {5 a b^4}{6 x^6}-\frac {b^5}{5 x^5} \]
[In]
[Out]
Rule 45
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {a^5}{x^{11}}+\frac {5 a^4 b}{x^{10}}+\frac {10 a^3 b^2}{x^9}+\frac {10 a^2 b^3}{x^8}+\frac {5 a b^4}{x^7}+\frac {b^5}{x^6}\right ) \, dx \\ & = -\frac {a^5}{10 x^{10}}-\frac {5 a^4 b}{9 x^9}-\frac {5 a^3 b^2}{4 x^8}-\frac {10 a^2 b^3}{7 x^7}-\frac {5 a b^4}{6 x^6}-\frac {b^5}{5 x^5} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.00 \[ \int \frac {(a+b x)^5}{x^{11}} \, dx=-\frac {a^5}{10 x^{10}}-\frac {5 a^4 b}{9 x^9}-\frac {5 a^3 b^2}{4 x^8}-\frac {10 a^2 b^3}{7 x^7}-\frac {5 a b^4}{6 x^6}-\frac {b^5}{5 x^5} \]
[In]
[Out]
Time = 0.16 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.83
method | result | size |
norman | \(\frac {-\frac {1}{5} b^{5} x^{5}-\frac {5}{6} a \,b^{4} x^{4}-\frac {10}{7} a^{2} b^{3} x^{3}-\frac {5}{4} a^{3} b^{2} x^{2}-\frac {5}{9} a^{4} b x -\frac {1}{10} a^{5}}{x^{10}}\) | \(57\) |
risch | \(\frac {-\frac {1}{5} b^{5} x^{5}-\frac {5}{6} a \,b^{4} x^{4}-\frac {10}{7} a^{2} b^{3} x^{3}-\frac {5}{4} a^{3} b^{2} x^{2}-\frac {5}{9} a^{4} b x -\frac {1}{10} a^{5}}{x^{10}}\) | \(57\) |
gosper | \(-\frac {252 b^{5} x^{5}+1050 a \,b^{4} x^{4}+1800 a^{2} b^{3} x^{3}+1575 a^{3} b^{2} x^{2}+700 a^{4} b x +126 a^{5}}{1260 x^{10}}\) | \(58\) |
default | \(-\frac {a^{5}}{10 x^{10}}-\frac {5 a^{4} b}{9 x^{9}}-\frac {5 a^{3} b^{2}}{4 x^{8}}-\frac {10 a^{2} b^{3}}{7 x^{7}}-\frac {5 a \,b^{4}}{6 x^{6}}-\frac {b^{5}}{5 x^{5}}\) | \(58\) |
parallelrisch | \(\frac {-252 b^{5} x^{5}-1050 a \,b^{4} x^{4}-1800 a^{2} b^{3} x^{3}-1575 a^{3} b^{2} x^{2}-700 a^{4} b x -126 a^{5}}{1260 x^{10}}\) | \(58\) |
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.83 \[ \int \frac {(a+b x)^5}{x^{11}} \, dx=-\frac {252 \, b^{5} x^{5} + 1050 \, a b^{4} x^{4} + 1800 \, a^{2} b^{3} x^{3} + 1575 \, a^{3} b^{2} x^{2} + 700 \, a^{4} b x + 126 \, a^{5}}{1260 \, x^{10}} \]
[In]
[Out]
Time = 0.24 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.88 \[ \int \frac {(a+b x)^5}{x^{11}} \, dx=\frac {- 126 a^{5} - 700 a^{4} b x - 1575 a^{3} b^{2} x^{2} - 1800 a^{2} b^{3} x^{3} - 1050 a b^{4} x^{4} - 252 b^{5} x^{5}}{1260 x^{10}} \]
[In]
[Out]
none
Time = 0.20 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.83 \[ \int \frac {(a+b x)^5}{x^{11}} \, dx=-\frac {252 \, b^{5} x^{5} + 1050 \, a b^{4} x^{4} + 1800 \, a^{2} b^{3} x^{3} + 1575 \, a^{3} b^{2} x^{2} + 700 \, a^{4} b x + 126 \, a^{5}}{1260 \, x^{10}} \]
[In]
[Out]
none
Time = 0.30 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.83 \[ \int \frac {(a+b x)^5}{x^{11}} \, dx=-\frac {252 \, b^{5} x^{5} + 1050 \, a b^{4} x^{4} + 1800 \, a^{2} b^{3} x^{3} + 1575 \, a^{3} b^{2} x^{2} + 700 \, a^{4} b x + 126 \, a^{5}}{1260 \, x^{10}} \]
[In]
[Out]
Time = 0.06 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.83 \[ \int \frac {(a+b x)^5}{x^{11}} \, dx=-\frac {\frac {a^5}{10}+\frac {5\,a^4\,b\,x}{9}+\frac {5\,a^3\,b^2\,x^2}{4}+\frac {10\,a^2\,b^3\,x^3}{7}+\frac {5\,a\,b^4\,x^4}{6}+\frac {b^5\,x^5}{5}}{x^{10}} \]
[In]
[Out]