Optimal. Leaf size=16 \[ \frac{x}{a \sqrt [4]{a+b x^4}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0019039, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {191} \[ \frac{x}{a \sqrt [4]{a+b x^4}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 191
Rubi steps
\begin{align*} \int \frac{1}{\left (a+b x^4\right )^{5/4}} \, dx &=\frac{x}{a \sqrt [4]{a+b x^4}}\\ \end{align*}
Mathematica [A] time = 0.0053008, size = 16, normalized size = 1. \[ \frac{x}{a \sqrt [4]{a+b x^4}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 15, normalized size = 0.9 \begin{align*}{\frac{x}{a}{\frac{1}{\sqrt [4]{b{x}^{4}+a}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.04094, size = 19, normalized size = 1.19 \begin{align*} \frac{x}{{\left (b x^{4} + a\right )}^{\frac{1}{4}} a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.4952, size = 50, normalized size = 3.12 \begin{align*} \frac{{\left (b x^{4} + a\right )}^{\frac{3}{4}} x}{a b x^{4} + a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.829706, size = 29, normalized size = 1.81 \begin{align*} \frac{x \Gamma \left (\frac{1}{4}\right )}{4 a^{\frac{5}{4}} \sqrt [4]{1 + \frac{b x^{4}}{a}} \Gamma \left (\frac{5}{4}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b x^{4} + a\right )}^{\frac{5}{4}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]