Optimal. Leaf size=27 \[ 3+e^3+25 (-2+x)^2-\frac {3 x^2-\log (x)}{x} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 15, normalized size of antiderivative = 0.56, number of steps
used = 5, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {14, 2341}
\begin {gather*} 25 x^2-103 x+\frac {\log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1-103 x^2+50 x^3}{x^2}-\frac {\log (x)}{x^2}\right ) \, dx\\ &=\int \frac {1-103 x^2+50 x^3}{x^2} \, dx-\int \frac {\log (x)}{x^2} \, dx\\ &=\frac {1}{x}+\frac {\log (x)}{x}+\int \left (-103+\frac {1}{x^2}+50 x\right ) \, dx\\ &=-103 x+25 x^2+\frac {\log (x)}{x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 15, normalized size = 0.56 \begin {gather*} -103 x+25 x^2+\frac {\log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.01, size = 16, normalized size = 0.59
method | result | size |
default | \(25 x^{2}-103 x +\frac {\ln \left (x \right )}{x}\) | \(16\) |
risch | \(25 x^{2}-103 x +\frac {\ln \left (x \right )}{x}\) | \(16\) |
norman | \(\frac {-103 x^{2}+25 x^{3}+\ln \left (x \right )}{x}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 15, normalized size = 0.56 \begin {gather*} 25 \, x^{2} - 103 \, x + \frac {\log \left (x\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.45, size = 17, normalized size = 0.63 \begin {gather*} \frac {25 \, x^{3} - 103 \, x^{2} + \log \left (x\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 12, normalized size = 0.44 \begin {gather*} 25 x^{2} - 103 x + \frac {\log {\left (x \right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 15, normalized size = 0.56 \begin {gather*} 25 \, x^{2} - 103 \, x + \frac {\log \left (x\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 6.54, size = 14, normalized size = 0.52 \begin {gather*} x\,\left (25\,x-103\right )+\frac {\ln \left (x\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________