Optimal. Leaf size=18 \[ -\frac{2 \sqrt{x^5+1}}{5 x^{5/2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0029125, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {264} \[ -\frac{2 \sqrt{x^5+1}}{5 x^{5/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^{7/2} \sqrt{1+x^5}} \, dx &=-\frac{2 \sqrt{1+x^5}}{5 x^{5/2}}\\ \end{align*}
Mathematica [A] time = 0.0033145, size = 18, normalized size = 1. \[ -\frac{2 \sqrt{x^5+1}}{5 x^{5/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0.003, size = 32, normalized size = 1.8 \begin{align*} -{\frac{ \left ( 2+2\,x \right ) \left ({x}^{4}-{x}^{3}+{x}^{2}-x+1 \right ) }{5}{x}^{-{\frac{5}{2}}}{\frac{1}{\sqrt{{x}^{5}+1}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.973099, size = 16, normalized size = 0.89 \begin{align*} -\frac{2 \, \sqrt{x^{5} + 1}}{5 \, x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.77472, size = 38, normalized size = 2.11 \begin{align*} -\frac{2 \, \sqrt{x^{5} + 1}}{5 \, x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 22.2405, size = 14, normalized size = 0.78 \begin{align*} - \frac{2 \sqrt{1 + \frac{1}{x^{5}}}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.17961, size = 15, normalized size = 0.83 \begin{align*} -\frac{2}{5} \, \sqrt{\frac{1}{x^{5}} + 1} + \frac{2}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]