Optimal. Leaf size=26 \[ \frac {\left (1+x^4\right )^{3/4} \left (28+x^4-27 x^8\right )}{77 x^{11}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 33, normalized size of antiderivative = 1.27, number of steps
used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {464, 270}
\begin {gather*} \frac {4 \left (x^4+1\right )^{7/4}}{11 x^{11}}-\frac {27 \left (x^4+1\right )^{7/4}}{77 x^7} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 270
Rule 464
Rubi steps
\begin {align*} \int \frac {\left (-4+x^4\right ) \left (1+x^4\right )^{3/4}}{x^{12}} \, dx &=\frac {4 \left (1+x^4\right )^{7/4}}{11 x^{11}}+\frac {27}{11} \int \frac {\left (1+x^4\right )^{3/4}}{x^8} \, dx\\ &=\frac {4 \left (1+x^4\right )^{7/4}}{11 x^{11}}-\frac {27 \left (1+x^4\right )^{7/4}}{77 x^7}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.10, size = 23, normalized size = 0.88 \begin {gather*} \frac {\left (28-27 x^4\right ) \left (1+x^4\right )^{7/4}}{77 x^{11}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.26, size = 20, normalized size = 0.77
method | result | size |
gosper | \(-\frac {\left (27 x^{4}-28\right ) \left (x^{4}+1\right )^{\frac {7}{4}}}{77 x^{11}}\) | \(20\) |
trager | \(-\frac {\left (27 x^{8}-x^{4}-28\right ) \left (x^{4}+1\right )^{\frac {3}{4}}}{77 x^{11}}\) | \(25\) |
risch | \(-\frac {27 x^{12}+26 x^{8}-29 x^{4}-28}{77 x^{11} \left (x^{4}+1\right )^{\frac {1}{4}}}\) | \(30\) |
meijerg | \(\frac {4 \left (-\frac {4}{7} x^{8}+\frac {3}{7} x^{4}+1\right ) \left (x^{4}+1\right )^{\frac {3}{4}}}{11 x^{11}}-\frac {\left (x^{4}+1\right )^{\frac {7}{4}}}{7 x^{7}}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 25, normalized size = 0.96 \begin {gather*} -\frac {5 \, {\left (x^{4} + 1\right )}^{\frac {7}{4}}}{7 \, x^{7}} + \frac {4 \, {\left (x^{4} + 1\right )}^{\frac {11}{4}}}{11 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 24, normalized size = 0.92 \begin {gather*} -\frac {{\left (27 \, x^{8} - x^{4} - 28\right )} {\left (x^{4} + 1\right )}^{\frac {3}{4}}}{77 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 136 vs.
\(2 (22) = 44\).
time = 2.23, size = 136, normalized size = 5.23 \begin {gather*} \frac {\left (1 + \frac {1}{x^{4}}\right )^{\frac {3}{4}} \Gamma \left (- \frac {7}{4}\right )}{4 \Gamma \left (- \frac {3}{4}\right )} - \frac {\left (x^{4} + 1\right )^{\frac {3}{4}} \Gamma \left (- \frac {11}{4}\right )}{x^{3} \Gamma \left (- \frac {3}{4}\right )} + \frac {\left (1 + \frac {1}{x^{4}}\right )^{\frac {3}{4}} \Gamma \left (- \frac {7}{4}\right )}{4 x^{4} \Gamma \left (- \frac {3}{4}\right )} + \frac {3 \left (x^{4} + 1\right )^{\frac {3}{4}} \Gamma \left (- \frac {11}{4}\right )}{4 x^{7} \Gamma \left (- \frac {3}{4}\right )} + \frac {7 \left (x^{4} + 1\right )^{\frac {3}{4}} \Gamma \left (- \frac {11}{4}\right )}{4 x^{11} \Gamma \left (- \frac {3}{4}\right )} \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.31, size = 38, normalized size = 1.46 \begin {gather*} \frac {28\,{\left (x^4+1\right )}^{3/4}+x^4\,{\left (x^4+1\right )}^{3/4}-27\,x^8\,{\left (x^4+1\right )}^{3/4}}{77\,x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________