Optimal. Leaf size=30 \[ -\frac{a^2}{5 x^5}-\frac{a b}{2 x^4}-\frac{b^2}{3 x^3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0080537, antiderivative size = 30, 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} \[ -\frac{a^2}{5 x^5}-\frac{a b}{2 x^4}-\frac{b^2}{3 x^3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^2}{x^6} \, dx &=\int \left (\frac{a^2}{x^6}+\frac{2 a b}{x^5}+\frac{b^2}{x^4}\right ) \, dx\\ &=-\frac{a^2}{5 x^5}-\frac{a b}{2 x^4}-\frac{b^2}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0078579, size = 30, normalized size = 1. \[ -\frac{a^2}{5 x^5}-\frac{a b}{2 x^4}-\frac{b^2}{3 x^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 25, normalized size = 0.8 \begin{align*} -{\frac{{a}^{2}}{5\,{x}^{5}}}-{\frac{ab}{2\,{x}^{4}}}-{\frac{{b}^{2}}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.0103, size = 32, normalized size = 1.07 \begin{align*} -\frac{10 \, b^{2} x^{2} + 15 \, a b x + 6 \, a^{2}}{30 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.49608, size = 58, normalized size = 1.93 \begin{align*} -\frac{10 \, b^{2} x^{2} + 15 \, a b x + 6 \, a^{2}}{30 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.464478, size = 26, normalized size = 0.87 \begin{align*} - \frac{6 a^{2} + 15 a b x + 10 b^{2} x^{2}}{30 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.19931, size = 32, normalized size = 1.07 \begin{align*} -\frac{10 \, b^{2} x^{2} + 15 \, a b x + 6 \, a^{2}}{30 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]