Optimal. Leaf size=23 \[ \frac {\log (x)}{a}-\frac {\log \left (a-b x^3\right )}{3 a} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 4, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {272, 36, 29, 31}
\begin {gather*} \frac {\log (x)}{a}-\frac {\log \left (a-b x^3\right )}{3 a} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 29
Rule 31
Rule 36
Rule 272
Rubi steps
\begin {align*} \int \frac {1}{x \left (a-b x^3\right )} \, dx &=\frac {1}{3} \text {Subst}\left (\int \frac {1}{x (a-b x)} \, dx,x,x^3\right )\\ &=\frac {\text {Subst}\left (\int \frac {1}{x} \, dx,x,x^3\right )}{3 a}+\frac {b \text {Subst}\left (\int \frac {1}{a-b x} \, dx,x,x^3\right )}{3 a}\\ &=\frac {\log (x)}{a}-\frac {\log \left (a-b x^3\right )}{3 a}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 23, normalized size = 1.00 \begin {gather*} \frac {\log (x)}{a}-\frac {\log \left (a-b x^3\right )}{3 a} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.13, size = 22, normalized size = 0.96
method | result | size |
default | \(\frac {\ln \left (x \right )}{a}-\frac {\ln \left (-b \,x^{3}+a \right )}{3 a}\) | \(22\) |
norman | \(\frac {\ln \left (x \right )}{a}-\frac {\ln \left (-b \,x^{3}+a \right )}{3 a}\) | \(22\) |
risch | \(\frac {\ln \left (x \right )}{a}-\frac {\ln \left (-b \,x^{3}+a \right )}{3 a}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.30, size = 25, normalized size = 1.09 \begin {gather*} -\frac {\log \left (b x^{3} - a\right )}{3 \, a} + \frac {\log \left (x^{3}\right )}{3 \, a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 20, normalized size = 0.87 \begin {gather*} -\frac {\log \left (b x^{3} - a\right ) - 3 \, \log \left (x\right )}{3 \, a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.11, size = 15, normalized size = 0.65 \begin {gather*} \frac {\log {\left (x \right )}}{a} - \frac {\log {\left (- \frac {a}{b} + x^{3} \right )}}{3 a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.98, size = 24, normalized size = 1.04 \begin {gather*} -\frac {\log \left ({\left | b x^{3} - a \right |}\right )}{3 \, a} + \frac {\log \left ({\left | x \right |}\right )}{a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.10, size = 21, normalized size = 0.91 \begin {gather*} \frac {\ln \left (x\right )}{a}-\frac {\ln \left (a-b\,x^3\right )}{3\,a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________