Optimal. Leaf size=18 \[ \frac {x^5}{5}-\frac {1}{5} \log \left (1+x^5\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {272, 45}
\begin {gather*} \frac {x^5}{5}-\frac {1}{5} \log \left (x^5+1\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 45
Rule 272
Rubi steps
\begin {align*} \int \frac {x^9}{1+x^5} \, dx &=\frac {1}{5} \text {Subst}\left (\int \frac {x}{1+x} \, dx,x,x^5\right )\\ &=\frac {1}{5} \text {Subst}\left (\int \left (1+\frac {1}{-1-x}\right ) \, dx,x,x^5\right )\\ &=\frac {x^5}{5}-\frac {1}{5} \log \left (1+x^5\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 18, normalized size = 1.00 \begin {gather*} \frac {x^5}{5}-\frac {1}{5} \log \left (1+x^5\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.15, size = 15, normalized size = 0.83
method | result | size |
default | \(\frac {x^{5}}{5}-\frac {\ln \left (x^{5}+1\right )}{5}\) | \(15\) |
meijerg | \(\frac {x^{5}}{5}-\frac {\ln \left (x^{5}+1\right )}{5}\) | \(15\) |
risch | \(\frac {x^{5}}{5}-\frac {\ln \left (x^{5}+1\right )}{5}\) | \(15\) |
norman | \(\frac {x^{5}}{5}-\frac {\ln \left (x +1\right )}{5}-\frac {\ln \left (x^{4}-x^{3}+x^{2}-x +1\right )}{5}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 14, normalized size = 0.78 \begin {gather*} \frac {1}{5} \, x^{5} - \frac {1}{5} \, \log \left (x^{5} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 14, normalized size = 0.78 \begin {gather*} \frac {1}{5} \, x^{5} - \frac {1}{5} \, \log \left (x^{5} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 12, normalized size = 0.67 \begin {gather*} \frac {x^{5}}{5} - \frac {\log {\left (x^{5} + 1 \right )}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 2.15, size = 15, normalized size = 0.83 \begin {gather*} \frac {1}{5} \, x^{5} - \frac {1}{5} \, \log \left ({\left | x^{5} + 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 14, normalized size = 0.78 \begin {gather*} \frac {x^5}{5}-\frac {\ln \left (x^5+1\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________