Optimal. Leaf size=87 \[ -\frac {a^6 c^5}{10 x^{10}}+\frac {4 a^5 b c^5}{9 x^9}-\frac {5 a^4 b^2 c^5}{8 x^8}+\frac {5 a^2 b^4 c^5}{6 x^6}-\frac {4 a b^5 c^5}{5 x^5}+\frac {b^6 c^5}{4 x^4} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 87, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {75} \[ -\frac {5 a^4 b^2 c^5}{8 x^8}+\frac {5 a^2 b^4 c^5}{6 x^6}+\frac {4 a^5 b c^5}{9 x^9}-\frac {a^6 c^5}{10 x^{10}}-\frac {4 a b^5 c^5}{5 x^5}+\frac {b^6 c^5}{4 x^4} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 75
Rubi steps
\begin {align*} \int \frac {(a+b x) (a c-b c x)^5}{x^{11}} \, dx &=\int \left (\frac {a^6 c^5}{x^{11}}-\frac {4 a^5 b c^5}{x^{10}}+\frac {5 a^4 b^2 c^5}{x^9}-\frac {5 a^2 b^4 c^5}{x^7}+\frac {4 a b^5 c^5}{x^6}-\frac {b^6 c^5}{x^5}\right ) \, dx\\ &=-\frac {a^6 c^5}{10 x^{10}}+\frac {4 a^5 b c^5}{9 x^9}-\frac {5 a^4 b^2 c^5}{8 x^8}+\frac {5 a^2 b^4 c^5}{6 x^6}-\frac {4 a b^5 c^5}{5 x^5}+\frac {b^6 c^5}{4 x^4}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 73, normalized size = 0.84 \[ c^5 \left (-\frac {a^6}{10 x^{10}}+\frac {4 a^5 b}{9 x^9}-\frac {5 a^4 b^2}{8 x^8}+\frac {5 a^2 b^4}{6 x^6}-\frac {4 a b^5}{5 x^5}+\frac {b^6}{4 x^4}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.64, size = 75, normalized size = 0.86 \[ \frac {90 \, b^{6} c^{5} x^{6} - 288 \, a b^{5} c^{5} x^{5} + 300 \, a^{2} b^{4} c^{5} x^{4} - 225 \, a^{4} b^{2} c^{5} x^{2} + 160 \, a^{5} b c^{5} x - 36 \, a^{6} c^{5}}{360 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.91, size = 75, normalized size = 0.86 \[ \frac {90 \, b^{6} c^{5} x^{6} - 288 \, a b^{5} c^{5} x^{5} + 300 \, a^{2} b^{4} c^{5} x^{4} - 225 \, a^{4} b^{2} c^{5} x^{2} + 160 \, a^{5} b c^{5} x - 36 \, a^{6} c^{5}}{360 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 62, normalized size = 0.71 \[ \left (\frac {b^{6}}{4 x^{4}}-\frac {4 a \,b^{5}}{5 x^{5}}+\frac {5 a^{2} b^{4}}{6 x^{6}}-\frac {5 a^{4} b^{2}}{8 x^{8}}+\frac {4 a^{5} b}{9 x^{9}}-\frac {a^{6}}{10 x^{10}}\right ) c^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.09, size = 75, normalized size = 0.86 \[ \frac {90 \, b^{6} c^{5} x^{6} - 288 \, a b^{5} c^{5} x^{5} + 300 \, a^{2} b^{4} c^{5} x^{4} - 225 \, a^{4} b^{2} c^{5} x^{2} + 160 \, a^{5} b c^{5} x - 36 \, a^{6} c^{5}}{360 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 75, normalized size = 0.86 \[ -\frac {\frac {a^6\,c^5}{10}-\frac {4\,a^5\,b\,c^5\,x}{9}+\frac {5\,a^4\,b^2\,c^5\,x^2}{8}-\frac {5\,a^2\,b^4\,c^5\,x^4}{6}+\frac {4\,a\,b^5\,c^5\,x^5}{5}-\frac {b^6\,c^5\,x^6}{4}}{x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.56, size = 82, normalized size = 0.94 \[ - \frac {36 a^{6} c^{5} - 160 a^{5} b c^{5} x + 225 a^{4} b^{2} c^{5} x^{2} - 300 a^{2} b^{4} c^{5} x^{4} + 288 a b^{5} c^{5} x^{5} - 90 b^{6} c^{5} x^{6}}{360 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________