Optimal. Leaf size=24 \[ \frac {150 \left (4+5 x+3 \left (x^2+\log \left (\frac {x^2}{3}\right )\right )\right )}{x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.38, number of steps
used = 4, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {14, 37, 2341}
\begin {gather*} \frac {75 (5 x+2)^2}{2 x^2}+\frac {450}{x^2}+\frac {450 \log \left (\frac {x^2}{3}\right )}{x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rule 37
Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {150 (2+5 x)}{x^3}-\frac {900 \log \left (\frac {x^2}{3}\right )}{x^3}\right ) \, dx\\ &=-\left (150 \int \frac {2+5 x}{x^3} \, dx\right )-900 \int \frac {\log \left (\frac {x^2}{3}\right )}{x^3} \, dx\\ &=\frac {450}{x^2}+\frac {75 (2+5 x)^2}{2 x^2}+\frac {450 \log \left (\frac {x^2}{3}\right )}{x^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 24, normalized size = 1.00 \begin {gather*} \frac {600}{x^2}+\frac {750}{x}+\frac {450 \log \left (\frac {x^2}{3}\right )}{x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.19, size = 28, normalized size = 1.17
method | result | size |
norman | \(\frac {600+750 x +450 \ln \left (\frac {x^{2}}{3}\right )}{x^{2}}\) | \(18\) |
risch | \(\frac {450 \ln \left (\frac {x^{2}}{3}\right )}{x^{2}}+\frac {750 x +600}{x^{2}}\) | \(23\) |
default | \(-\frac {450 \ln \left (3\right )}{x^{2}}+\frac {450 \ln \left (x^{2}\right )}{x^{2}}+\frac {600}{x^{2}}+\frac {750}{x}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 22, normalized size = 0.92 \begin {gather*} \frac {750}{x} + \frac {450 \, \log \left (\frac {1}{3} \, x^{2}\right )}{x^{2}} + \frac {600}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.43, size = 18, normalized size = 0.75 \begin {gather*} \frac {150 \, {\left (5 \, x + 3 \, \log \left (\frac {1}{3} \, x^{2}\right ) + 4\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 20, normalized size = 0.83 \begin {gather*} - \frac {- 750 x - 600}{x^{2}} + \frac {450 \log {\left (\frac {x^{2}}{3} \right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 22, normalized size = 0.92 \begin {gather*} \frac {150 \, {\left (5 \, x + 4\right )}}{x^{2}} + \frac {450 \, \log \left (\frac {1}{3} \, x^{2}\right )}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.05, size = 16, normalized size = 0.67 \begin {gather*} \frac {150\,\left (5\,x+\ln \left (\frac {x^6}{27}\right )+4\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________