Optimal. Leaf size=15 \[ \frac{\log \left (a+c x^4\right )}{4 c} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0032196, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {260} \[ \frac{\log \left (a+c x^4\right )}{4 c} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 260
Rubi steps
\begin{align*} \int \frac{x^3}{a+c x^4} \, dx &=\frac{\log \left (a+c x^4\right )}{4 c}\\ \end{align*}
Mathematica [A] time = 0.0034486, size = 15, normalized size = 1. \[ \frac{\log \left (a+c x^4\right )}{4 c} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 14, normalized size = 0.9 \begin{align*}{\frac{\ln \left ( c{x}^{4}+a \right ) }{4\,c}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.963588, size = 18, normalized size = 1.2 \begin{align*} \frac{\log \left (c x^{4} + a\right )}{4 \, c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.59236, size = 30, normalized size = 2. \begin{align*} \frac{\log \left (c x^{4} + a\right )}{4 \, c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.192819, size = 10, normalized size = 0.67 \begin{align*} \frac{\log{\left (a + c x^{4} \right )}}{4 c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.12585, size = 19, normalized size = 1.27 \begin{align*} \frac{\log \left ({\left | c x^{4} + a \right |}\right )}{4 \, c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]