Optimal. Leaf size=16 \[ -\frac {\left (x^4+1\right )^{3/4}}{3 x^3} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, 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 = {264} \begin {gather*} -\frac {\left (x^4+1\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 264
Rubi steps
\begin {align*} \int \frac {1}{x^4 \sqrt [4]{1+x^4}} \, dx &=-\frac {\left (1+x^4\right )^{3/4}}{3 x^3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} -\frac {\left (x^4+1\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.12, size = 16, normalized size = 1.00 \begin {gather*} -\frac {\left (1+x^4\right )^{3/4}}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.43, size = 12, normalized size = 0.75 \begin {gather*} -\frac {{\left (x^{4} + 1\right )}^{\frac {3}{4}}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{{\left (x^{4} + 1\right )}^{\frac {1}{4}} x^{4}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 13, normalized size = 0.81
method | result | size |
gosper | \(-\frac {\left (x^{4}+1\right )^{\frac {3}{4}}}{3 x^{3}}\) | \(13\) |
trager | \(-\frac {\left (x^{4}+1\right )^{\frac {3}{4}}}{3 x^{3}}\) | \(13\) |
meijerg | \(-\frac {\left (x^{4}+1\right )^{\frac {3}{4}}}{3 x^{3}}\) | \(13\) |
risch | \(-\frac {\left (x^{4}+1\right )^{\frac {3}{4}}}{3 x^{3}}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.42, size = 12, normalized size = 0.75 \begin {gather*} -\frac {{\left (x^{4} + 1\right )}^{\frac {3}{4}}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.16, size = 12, normalized size = 0.75 \begin {gather*} -\frac {{\left (x^4+1\right )}^{3/4}}{3\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.58, size = 22, normalized size = 1.38 \begin {gather*} \frac {\left (1 + \frac {1}{x^{4}}\right )^{\frac {3}{4}} \Gamma \left (- \frac {3}{4}\right )}{4 \Gamma \left (\frac {1}{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________