Optimal. Leaf size=67 \[ -\frac{10 a^3 b^2}{11 x^{11}}-\frac{a^2 b^3}{x^{10}}-\frac{5 a^4 b}{12 x^{12}}-\frac{a^5}{13 x^{13}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{8 x^8} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0215932, antiderivative size = 67, normalized size of antiderivative = 1., 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} \[ -\frac{10 a^3 b^2}{11 x^{11}}-\frac{a^2 b^3}{x^{10}}-\frac{5 a^4 b}{12 x^{12}}-\frac{a^5}{13 x^{13}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{8 x^8} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^5}{x^{14}} \, dx &=\int \left (\frac{a^5}{x^{14}}+\frac{5 a^4 b}{x^{13}}+\frac{10 a^3 b^2}{x^{12}}+\frac{10 a^2 b^3}{x^{11}}+\frac{5 a b^4}{x^{10}}+\frac{b^5}{x^9}\right ) \, dx\\ &=-\frac{a^5}{13 x^{13}}-\frac{5 a^4 b}{12 x^{12}}-\frac{10 a^3 b^2}{11 x^{11}}-\frac{a^2 b^3}{x^{10}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{8 x^8}\\ \end{align*}
Mathematica [A] time = 0.0044323, size = 67, normalized size = 1. \[ -\frac{10 a^3 b^2}{11 x^{11}}-\frac{a^2 b^3}{x^{10}}-\frac{5 a^4 b}{12 x^{12}}-\frac{a^5}{13 x^{13}}-\frac{5 a b^4}{9 x^9}-\frac{b^5}{8 x^8} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 58, normalized size = 0.9 \begin{align*} -{\frac{{a}^{5}}{13\,{x}^{13}}}-{\frac{5\,{a}^{4}b}{12\,{x}^{12}}}-{\frac{10\,{a}^{3}{b}^{2}}{11\,{x}^{11}}}-{\frac{{a}^{2}{b}^{3}}{{x}^{10}}}-{\frac{5\,a{b}^{4}}{9\,{x}^{9}}}-{\frac{{b}^{5}}{8\,{x}^{8}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.06149, size = 77, normalized size = 1.15 \begin{align*} -\frac{1287 \, b^{5} x^{5} + 5720 \, a b^{4} x^{4} + 10296 \, a^{2} b^{3} x^{3} + 9360 \, a^{3} b^{2} x^{2} + 4290 \, a^{4} b x + 792 \, a^{5}}{10296 \, x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.42976, size = 150, normalized size = 2.24 \begin{align*} -\frac{1287 \, b^{5} x^{5} + 5720 \, a b^{4} x^{4} + 10296 \, a^{2} b^{3} x^{3} + 9360 \, a^{3} b^{2} x^{2} + 4290 \, a^{4} b x + 792 \, a^{5}}{10296 \, x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.930171, size = 61, normalized size = 0.91 \begin{align*} - \frac{792 a^{5} + 4290 a^{4} b x + 9360 a^{3} b^{2} x^{2} + 10296 a^{2} b^{3} x^{3} + 5720 a b^{4} x^{4} + 1287 b^{5} x^{5}}{10296 x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.20667, size = 77, normalized size = 1.15 \begin{align*} -\frac{1287 \, b^{5} x^{5} + 5720 \, a b^{4} x^{4} + 10296 \, a^{2} b^{3} x^{3} + 9360 \, a^{3} b^{2} x^{2} + 4290 \, a^{4} b x + 792 \, a^{5}}{10296 \, x^{13}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]