Optimal. Leaf size=16 \[ 3+e^{\log ^2(x)}-2 x-5 x^2 \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.04, antiderivative size = 18, normalized size of antiderivative = 1.12, number of steps
used = 4, number of rules used = 4, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.174, Rules used = {14, 2308, 2235,
2240} \begin {gather*} e^{\log ^2(x)}-\frac {1}{5} (5 x+1)^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rule 2235
Rule 2240
Rule 2308
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 (1+5 x)+\frac {2 e^{\log ^2(x)} \log (x)}{x}\right ) \, dx\\ &=-\frac {1}{5} (1+5 x)^2+2 \int \frac {e^{\log ^2(x)} \log (x)}{x} \, dx\\ &=-\frac {1}{5} (1+5 x)^2+2 \text {Subst}\left (\int e^{x^2} x \, dx,x,\log (x)\right )\\ &=e^{\log ^2(x)}-\frac {1}{5} (1+5 x)^2\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 15, normalized size = 0.94 \begin {gather*} e^{\log ^2(x)}-2 x-5 x^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.03, size = 15, normalized size = 0.94
method | result | size |
default | \(-2 x +{\mathrm e}^{\ln \left (x \right )^{2}}-5 x^{2}\) | \(15\) |
norman | \(-2 x +{\mathrm e}^{\ln \left (x \right )^{2}}-5 x^{2}\) | \(15\) |
risch | \(-2 x +{\mathrm e}^{\ln \left (x \right )^{2}}-5 x^{2}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 14, normalized size = 0.88 \begin {gather*} -5 \, x^{2} - 2 \, x + e^{\left (\log \left (x\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 14, normalized size = 0.88 \begin {gather*} -5 \, x^{2} - 2 \, x + e^{\left (\log \left (x\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 14, normalized size = 0.88 \begin {gather*} - 5 x^{2} - 2 x + e^{\log {\left (x \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 14, normalized size = 0.88 \begin {gather*} -5 \, x^{2} - 2 \, x + e^{\left (\log \left (x\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.75, size = 14, normalized size = 0.88 \begin {gather*} {\mathrm {e}}^{{\ln \left (x\right )}^2}-2\,x-5\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________