Optimal. Leaf size=69 \[ -\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{4 x^8}-\frac{a^4 b}{2 x^{10}}-\frac{a^5}{11 x^{11}}-\frac{5 a b^4}{7 x^7}-\frac{b^5}{6 x^6} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.020542, antiderivative size = 69, 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} \[ -\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{4 x^8}-\frac{a^4 b}{2 x^{10}}-\frac{a^5}{11 x^{11}}-\frac{5 a b^4}{7 x^7}-\frac{b^5}{6 x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^5}{x^{12}} \, dx &=\int \left (\frac{a^5}{x^{12}}+\frac{5 a^4 b}{x^{11}}+\frac{10 a^3 b^2}{x^{10}}+\frac{10 a^2 b^3}{x^9}+\frac{5 a b^4}{x^8}+\frac{b^5}{x^7}\right ) \, dx\\ &=-\frac{a^5}{11 x^{11}}-\frac{a^4 b}{2 x^{10}}-\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{4 x^8}-\frac{5 a b^4}{7 x^7}-\frac{b^5}{6 x^6}\\ \end{align*}
Mathematica [A] time = 0.0041838, size = 69, normalized size = 1. \[ -\frac{10 a^3 b^2}{9 x^9}-\frac{5 a^2 b^3}{4 x^8}-\frac{a^4 b}{2 x^{10}}-\frac{a^5}{11 x^{11}}-\frac{5 a b^4}{7 x^7}-\frac{b^5}{6 x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 58, normalized size = 0.8 \begin{align*} -{\frac{{a}^{5}}{11\,{x}^{11}}}-{\frac{{a}^{4}b}{2\,{x}^{10}}}-{\frac{10\,{a}^{3}{b}^{2}}{9\,{x}^{9}}}-{\frac{5\,{a}^{2}{b}^{3}}{4\,{x}^{8}}}-{\frac{5\,a{b}^{4}}{7\,{x}^{7}}}-{\frac{{b}^{5}}{6\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.07538, size = 77, normalized size = 1.12 \begin{align*} -\frac{462 \, b^{5} x^{5} + 1980 \, a b^{4} x^{4} + 3465 \, a^{2} b^{3} x^{3} + 3080 \, a^{3} b^{2} x^{2} + 1386 \, a^{4} b x + 252 \, a^{5}}{2772 \, x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.56253, size = 146, normalized size = 2.12 \begin{align*} -\frac{462 \, b^{5} x^{5} + 1980 \, a b^{4} x^{4} + 3465 \, a^{2} b^{3} x^{3} + 3080 \, a^{3} b^{2} x^{2} + 1386 \, a^{4} b x + 252 \, a^{5}}{2772 \, x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.826751, size = 61, normalized size = 0.88 \begin{align*} - \frac{252 a^{5} + 1386 a^{4} b x + 3080 a^{3} b^{2} x^{2} + 3465 a^{2} b^{3} x^{3} + 1980 a b^{4} x^{4} + 462 b^{5} x^{5}}{2772 x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.17135, size = 77, normalized size = 1.12 \begin{align*} -\frac{462 \, b^{5} x^{5} + 1980 \, a b^{4} x^{4} + 3465 \, a^{2} b^{3} x^{3} + 3080 \, a^{3} b^{2} x^{2} + 1386 \, a^{4} b x + 252 \, a^{5}}{2772 \, x^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]