Optimal. Leaf size=43 \[ -\frac{3 a^2 b}{8 x^8}-\frac{a^3}{9 x^9}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{6 x^6} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0140346, antiderivative size = 43, 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} \[ -\frac{3 a^2 b}{8 x^8}-\frac{a^3}{9 x^9}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{6 x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^3}{x^{10}} \, dx &=\int \left (\frac{a^3}{x^{10}}+\frac{3 a^2 b}{x^9}+\frac{3 a b^2}{x^8}+\frac{b^3}{x^7}\right ) \, dx\\ &=-\frac{a^3}{9 x^9}-\frac{3 a^2 b}{8 x^8}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{6 x^6}\\ \end{align*}
Mathematica [A] time = 0.0036274, size = 43, normalized size = 1. \[ -\frac{3 a^2 b}{8 x^8}-\frac{a^3}{9 x^9}-\frac{3 a b^2}{7 x^7}-\frac{b^3}{6 x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 36, normalized size = 0.8 \begin{align*} -{\frac{{a}^{3}}{9\,{x}^{9}}}-{\frac{3\,{a}^{2}b}{8\,{x}^{8}}}-{\frac{3\,{b}^{2}a}{7\,{x}^{7}}}-{\frac{{b}^{3}}{6\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.10647, size = 47, normalized size = 1.09 \begin{align*} -\frac{84 \, b^{3} x^{3} + 216 \, a b^{2} x^{2} + 189 \, a^{2} b x + 56 \, a^{3}}{504 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.70502, size = 86, normalized size = 2. \begin{align*} -\frac{84 \, b^{3} x^{3} + 216 \, a b^{2} x^{2} + 189 \, a^{2} b x + 56 \, a^{3}}{504 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.540495, size = 37, normalized size = 0.86 \begin{align*} - \frac{56 a^{3} + 189 a^{2} b x + 216 a b^{2} x^{2} + 84 b^{3} x^{3}}{504 x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.14324, size = 47, normalized size = 1.09 \begin{align*} -\frac{84 \, b^{3} x^{3} + 216 \, a b^{2} x^{2} + 189 \, a^{2} b x + 56 \, a^{3}}{504 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]