Optimal. Leaf size=30 \[ \frac{a^2 x^6}{6}+\frac{2}{5} a b x^5+\frac{b^2 x^4}{4} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0140427, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {263, 43} \[ \frac{a^2 x^6}{6}+\frac{2}{5} a b x^5+\frac{b^2 x^4}{4} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 263
Rule 43
Rubi steps
\begin{align*} \int \left (a+\frac{b}{x}\right )^2 x^5 \, dx &=\int x^3 (b+a x)^2 \, dx\\ &=\int \left (b^2 x^3+2 a b x^4+a^2 x^5\right ) \, dx\\ &=\frac{b^2 x^4}{4}+\frac{2}{5} a b x^5+\frac{a^2 x^6}{6}\\ \end{align*}
Mathematica [A] time = 0.0017708, size = 30, normalized size = 1. \[ \frac{a^2 x^6}{6}+\frac{2}{5} a b x^5+\frac{b^2 x^4}{4} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 25, normalized size = 0.8 \begin{align*}{\frac{{b}^{2}{x}^{4}}{4}}+{\frac{2\,{x}^{5}ab}{5}}+{\frac{{a}^{2}{x}^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.943664, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{6} \, a^{2} x^{6} + \frac{2}{5} \, a b x^{5} + \frac{1}{4} \, b^{2} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.42873, size = 55, normalized size = 1.83 \begin{align*} \frac{1}{6} \, a^{2} x^{6} + \frac{2}{5} \, a b x^{5} + \frac{1}{4} \, b^{2} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.060149, size = 26, normalized size = 0.87 \begin{align*} \frac{a^{2} x^{6}}{6} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.15583, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{6} \, a^{2} x^{6} + \frac{2}{5} \, a b x^{5} + \frac{1}{4} \, b^{2} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]