Integrand size = 13, antiderivative size = 15 \[ \int \frac {1}{\left (a+\frac {b}{x^3}\right ) x^4} \, dx=-\frac {\log \left (a+\frac {b}{x^3}\right )}{3 b} \]
[Out]
Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {266} \[ \int \frac {1}{\left (a+\frac {b}{x^3}\right ) x^4} \, dx=-\frac {\log \left (a+\frac {b}{x^3}\right )}{3 b} \]
[In]
[Out]
Rule 266
Rubi steps \begin{align*} \text {integral}& = -\frac {\log \left (a+\frac {b}{x^3}\right )}{3 b} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.47 \[ \int \frac {1}{\left (a+\frac {b}{x^3}\right ) x^4} \, dx=\frac {\log (x)}{b}-\frac {\log \left (b+a x^3\right )}{3 b} \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93
method | result | size |
derivativedivides | \(-\frac {\ln \left (a +\frac {b}{x^{3}}\right )}{3 b}\) | \(14\) |
default | \(-\frac {\ln \left (a \,x^{3}+b \right )}{3 b}+\frac {\ln \left (x \right )}{b}\) | \(21\) |
norman | \(-\frac {\ln \left (a \,x^{3}+b \right )}{3 b}+\frac {\ln \left (x \right )}{b}\) | \(21\) |
risch | \(-\frac {\ln \left (a \,x^{3}+b \right )}{3 b}+\frac {\ln \left (x \right )}{b}\) | \(21\) |
parallelrisch | \(\frac {3 \ln \left (x \right )-\ln \left (a \,x^{3}+b \right )}{3 b}\) | \(21\) |
[In]
[Out]
none
Time = 0.29 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.20 \[ \int \frac {1}{\left (a+\frac {b}{x^3}\right ) x^4} \, dx=-\frac {\log \left (a x^{3} + b\right ) - 3 \, \log \left (x\right )}{3 \, b} \]
[In]
[Out]
Time = 0.12 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {1}{\left (a+\frac {b}{x^3}\right ) x^4} \, dx=\frac {\log {\left (x \right )}}{b} - \frac {\log {\left (x^{3} + \frac {b}{a} \right )}}{3 b} \]
[In]
[Out]
none
Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int \frac {1}{\left (a+\frac {b}{x^3}\right ) x^4} \, dx=-\frac {\log \left (a + \frac {b}{x^{3}}\right )}{3 \, b} \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.47 \[ \int \frac {1}{\left (a+\frac {b}{x^3}\right ) x^4} \, dx=-\frac {\log \left ({\left | a x^{3} + b \right |}\right )}{3 \, b} + \frac {\log \left ({\left | x \right |}\right )}{b} \]
[In]
[Out]
Time = 5.74 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.20 \[ \int \frac {1}{\left (a+\frac {b}{x^3}\right ) x^4} \, dx=-\frac {\ln \left (a\,x^3+b\right )-3\,\ln \left (x\right )}{3\,b} \]
[In]
[Out]