Optimal. Leaf size=21 \[ -\frac{\left (a+c x^4\right )^{3/2}}{6 a x^6} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0042621, antiderivative size = 21, 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} \[ -\frac{\left (a+c x^4\right )^{3/2}}{6 a x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin{align*} \int \frac{\sqrt{a+c x^4}}{x^7} \, dx &=-\frac{\left (a+c x^4\right )^{3/2}}{6 a x^6}\\ \end{align*}
Mathematica [A] time = 0.0045265, size = 21, normalized size = 1. \[ -\frac{\left (a+c x^4\right )^{3/2}}{6 a x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 18, normalized size = 0.9 \begin{align*} -{\frac{1}{6\,{x}^{6}a} \left ( c{x}^{4}+a \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.978639, size = 23, normalized size = 1.1 \begin{align*} -\frac{{\left (c x^{4} + a\right )}^{\frac{3}{2}}}{6 \, a x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.74164, size = 43, normalized size = 2.05 \begin{align*} -\frac{{\left (c x^{4} + a\right )}^{\frac{3}{2}}}{6 \, a x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.86008, size = 42, normalized size = 2. \begin{align*} - \frac{\sqrt{c} \sqrt{\frac{a}{c x^{4}} + 1}}{6 x^{4}} - \frac{c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{6 a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.27869, size = 19, normalized size = 0.9 \begin{align*} -\frac{{\left (c + \frac{a}{x^{4}}\right )}^{\frac{3}{2}}}{6 \, a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]