Optimal. Leaf size=20 \[ -\frac {x^2}{2}-\frac {1}{2} \log \left (1-x^2\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.231, Rules used = {1584, 266, 43} \[ -\frac {x^2}{2}-\frac {1}{2} \log \left (1-x^2\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rule 266
Rule 1584
Rubi steps
\begin {align*} \int \frac {x^4}{x-x^3} \, dx &=\int \frac {x^3}{1-x^2} \, dx\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {x}{1-x} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (-1+\frac {1}{1-x}\right ) \, dx,x,x^2\right )\\ &=-\frac {x^2}{2}-\frac {1}{2} \log \left (1-x^2\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 18, normalized size = 0.90 \[ -\frac {x^2}{2}-\frac {1}{2} \log \left (x^2-1\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.88, size = 14, normalized size = 0.70 \[ -\frac {1}{2} \, x^{2} - \frac {1}{2} \, \log \left (x^{2} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 15, normalized size = 0.75 \[ -\frac {1}{2} \, x^{2} - \frac {1}{2} \, \log \left ({\left | x^{2} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 19, normalized size = 0.95 \[ -\frac {x^{2}}{2}-\frac {\ln \left (x -1\right )}{2}-\frac {\ln \left (x +1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.32, size = 18, normalized size = 0.90 \[ -\frac {1}{2} \, x^{2} - \frac {1}{2} \, \log \left (x + 1\right ) - \frac {1}{2} \, \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 14, normalized size = 0.70 \[ -\frac {\ln \left (x^2-1\right )}{2}-\frac {x^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 14, normalized size = 0.70 \[ - \frac {x^{2}}{2} - \frac {\log {\left (x^{2} - 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________