Optimal. Leaf size=14 \[ \frac {1}{4} \log \left (2 (a+b)+x^4\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, 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 = {266}
\begin {gather*} \frac {1}{4} \log \left (2 (a+b)+x^4\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 266
Rubi steps
\begin {align*} \int \frac {x^3}{2 (a+b)+x^4} \, dx &=\frac {1}{4} \log \left (2 (a+b)+x^4\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 15, normalized size = 1.07 \begin {gather*} \frac {1}{4} \log \left (2 a+2 b+x^4\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.00, size = 14, normalized size = 1.00
method | result | size |
derivativedivides | \(\frac {\ln \left (x^{4}+2 a +2 b \right )}{4}\) | \(14\) |
default | \(\frac {\ln \left (x^{4}+2 a +2 b \right )}{4}\) | \(14\) |
norman | \(\frac {\ln \left (x^{4}+2 a +2 b \right )}{4}\) | \(14\) |
risch | \(\frac {\ln \left (x^{4}+2 a +2 b \right )}{4}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 13, normalized size = 0.93 \begin {gather*} \frac {1}{4} \, \log \left (x^{4} + 2 \, a + 2 \, b\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 13, normalized size = 0.93 \begin {gather*} \frac {1}{4} \, \log \left (x^{4} + 2 \, a + 2 \, b\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 12, normalized size = 0.86 \begin {gather*} \frac {\log {\left (2 a + 2 b + x^{4} \right )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {1}{4} \, \log \left ({\left | x^{4} + 2 \, a + 2 \, b \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.00, size = 13, normalized size = 0.93 \begin {gather*} \frac {\ln \left (x^4+2\,a+2\,b\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________