Optimal. Leaf size=23 \[ a^2 \log (x)+a b x^2+\frac{b^2 x^4}{4} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0072947, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {14} \[ a^2 \log (x)+a b x^2+\frac{b^2 x^4}{4} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin{align*} \int \frac{a^2+2 a b x^2+b^2 x^4}{x} \, dx &=\int \left (\frac{a^2}{x}+2 a b x+b^2 x^3\right ) \, dx\\ &=a b x^2+\frac{b^2 x^4}{4}+a^2 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0009761, size = 23, normalized size = 1. \[ a^2 \log (x)+a b x^2+\frac{b^2 x^4}{4} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.043, size = 22, normalized size = 1. \begin{align*} ab{x}^{2}+{\frac{{b}^{2}{x}^{4}}{4}}+{a}^{2}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.981399, size = 32, normalized size = 1.39 \begin{align*} \frac{1}{4} \, b^{2} x^{4} + a b x^{2} + \frac{1}{2} \, a^{2} \log \left (x^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.44811, size = 49, normalized size = 2.13 \begin{align*} \frac{1}{4} \, b^{2} x^{4} + a b x^{2} + a^{2} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.247208, size = 20, normalized size = 0.87 \begin{align*} a^{2} \log{\left (x \right )} + a b x^{2} + \frac{b^{2} x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.15573, size = 32, normalized size = 1.39 \begin{align*} \frac{1}{4} \, b^{2} x^{4} + a b x^{2} + \frac{1}{2} \, a^{2} \log \left (x^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]