Optimal. Leaf size=20 \[ a x+\frac{b x^3}{3}+\frac{c x^5}{5} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0056522, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {14} \[ a x+\frac{b x^3}{3}+\frac{c x^5}{5} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin{align*} \int \frac{a x+b x^3+c x^5}{x} \, dx &=\int \left (a+b x^2+c x^4\right ) \, dx\\ &=a x+\frac{b x^3}{3}+\frac{c x^5}{5}\\ \end{align*}
Mathematica [A] time = 0.0011684, size = 20, normalized size = 1. \[ a x+\frac{b x^3}{3}+\frac{c x^5}{5} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 17, normalized size = 0.9 \begin{align*} ax+{\frac{b{x}^{3}}{3}}+{\frac{c{x}^{5}}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.13096, size = 22, normalized size = 1.1 \begin{align*} \frac{1}{5} \, c x^{5} + \frac{1}{3} \, b x^{3} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.22959, size = 39, normalized size = 1.95 \begin{align*} \frac{1}{5} \, c x^{5} + \frac{1}{3} \, b x^{3} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.055914, size = 15, normalized size = 0.75 \begin{align*} a x + \frac{b x^{3}}{3} + \frac{c x^{5}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.09995, size = 22, normalized size = 1.1 \begin{align*} \frac{1}{5} \, c x^{5} + \frac{1}{3} \, b x^{3} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]