Optimal. Leaf size=26 \[ 3+e^{7 (x+x \log (x))}+\frac {1+2 (-4+x) (1+x)}{x} \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 0.10, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {7+2 x^2+e^{7 x+7 x \log (x)} \left (14 x^2+7 x^2 \log (x)\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {7+2 x^2}{x^2}+7 e^{7 x} x^{7 x} (2+\log (x))\right ) \, dx\\ &=7 \int e^{7 x} x^{7 x} (2+\log (x)) \, dx+\int \frac {7+2 x^2}{x^2} \, dx\\ &=7 \int \left (2 e^{7 x} x^{7 x}+e^{7 x} x^{7 x} \log (x)\right ) \, dx+\int \left (2+\frac {7}{x^2}\right ) \, dx\\ &=-\frac {7}{x}+2 x+7 \int e^{7 x} x^{7 x} \log (x) \, dx+14 \int e^{7 x} x^{7 x} \, dx\\ &=-\frac {7}{x}+2 x-7 \int \frac {\int e^{7 x} x^{7 x} \, dx}{x} \, dx+14 \int e^{7 x} x^{7 x} \, dx+(7 \log (x)) \int e^{7 x} x^{7 x} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.06, size = 20, normalized size = 0.77 \begin {gather*} -\frac {7}{x}+2 x+e^{7 x} x^{7 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.08, size = 20, normalized size = 0.77
method | result | size |
default | \({\mathrm e}^{7 x \ln \left (x \right )+7 x}+2 x -\frac {7}{x}\) | \(20\) |
risch | \(x^{7 x} {\mathrm e}^{7 x}+2 x -\frac {7}{x}\) | \(20\) |
norman | \(\frac {-7+x \,{\mathrm e}^{7 x \ln \left (x \right )+7 x}+2 x^{2}}{x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.34, size = 19, normalized size = 0.73 \begin {gather*} 2 \, x - \frac {7}{x} + e^{\left (7 \, x \log \left (x\right ) + 7 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.31, size = 23, normalized size = 0.88 \begin {gather*} \frac {2 \, x^{2} + x e^{\left (7 \, x \log \left (x\right ) + 7 \, x\right )} - 7}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.07, size = 17, normalized size = 0.65 \begin {gather*} 2 x + e^{7 x \log {\left (x \right )} + 7 x} - \frac {7}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 23, normalized size = 0.88 \begin {gather*} \frac {2 \, x^{2} + x e^{\left (7 \, x \log \left (x\right ) + 7 \, x\right )} - 7}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.48, size = 19, normalized size = 0.73 \begin {gather*} 2\,x+x^{7\,x}\,{\mathrm {e}}^{7\,x}-\frac {7}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________