Optimal. Leaf size=25 \[ \frac{a x^3}{3}+\frac{b x^5}{5}+\frac{c x^7}{7} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0072531, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {14} \[ \frac{a x^3}{3}+\frac{b x^5}{5}+\frac{c x^7}{7} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin{align*} \int x \left (a x+b x^3+c x^5\right ) \, dx &=\int \left (a x^2+b x^4+c x^6\right ) \, dx\\ &=\frac{a x^3}{3}+\frac{b x^5}{5}+\frac{c x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0018573, size = 25, normalized size = 1. \[ \frac{a x^3}{3}+\frac{b x^5}{5}+\frac{c x^7}{7} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 20, normalized size = 0.8 \begin{align*}{\frac{a{x}^{3}}{3}}+{\frac{b{x}^{5}}{5}}+{\frac{c{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.072, size = 26, normalized size = 1.04 \begin{align*} \frac{1}{7} \, c x^{7} + \frac{1}{5} \, b x^{5} + \frac{1}{3} \, a x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.08682, size = 47, normalized size = 1.88 \begin{align*} \frac{1}{7} x^{7} c + \frac{1}{5} x^{5} b + \frac{1}{3} x^{3} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.056432, size = 19, normalized size = 0.76 \begin{align*} \frac{a x^{3}}{3} + \frac{b x^{5}}{5} + \frac{c x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.0907, size = 26, normalized size = 1.04 \begin{align*} \frac{1}{7} \, c x^{7} + \frac{1}{5} \, b x^{5} + \frac{1}{3} \, a x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]