Optimal. Leaf size=22 \[ \frac {3}{2}-\frac {47}{2} \left (2+e^x\right ) x (x-\log (5)+\log (x)) \]
[Out]
________________________________________________________________________________________
Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(75\) vs. \(2(22)=44\).
time = 0.11, antiderivative size = 75, normalized size of antiderivative = 3.41, number of steps
used = 16, number of rules used = 5, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.102, Rules used = {12, 2227,
2225, 2207, 2634} \begin {gather*} -\frac {47}{2} e^x x^2-47 x^2+47 x-47 x \log (x)-47 x (1-\log (5))+\frac {47}{2} e^x \log (x)-\frac {47}{2} e^x (x+1) \log (x)-\frac {47}{2} e^x \log (5)+\frac {47}{2} e^x (x+1) \log (5) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2207
Rule 2225
Rule 2227
Rule 2634
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (-94-188 x+94 \log (5)+e^x \left (-47-94 x-47 x^2+(47+47 x) \log (5)\right )+\left (-94+e^x (-47-47 x)\right ) \log (x)\right ) \, dx\\ &=-47 x^2-47 x (1-\log (5))+\frac {1}{2} \int e^x \left (-47-94 x-47 x^2+(47+47 x) \log (5)\right ) \, dx+\frac {1}{2} \int \left (-94+e^x (-47-47 x)\right ) \log (x) \, dx\\ &=-47 x^2-47 x (1-\log (5))+\frac {47}{2} e^x \log (x)-47 x \log (x)-\frac {47}{2} e^x (1+x) \log (x)-\frac {1}{2} \int 47 \left (-2-e^x\right ) \, dx+\frac {1}{2} \int \left (-47 e^x-94 e^x x-47 e^x x^2+47 e^x (1+x) \log (5)\right ) \, dx\\ &=-47 x^2-47 x (1-\log (5))+\frac {47}{2} e^x \log (x)-47 x \log (x)-\frac {47}{2} e^x (1+x) \log (x)-\frac {47 \int e^x \, dx}{2}-\frac {47}{2} \int \left (-2-e^x\right ) \, dx-\frac {47}{2} \int e^x x^2 \, dx-47 \int e^x x \, dx+\frac {1}{2} (47 \log (5)) \int e^x (1+x) \, dx\\ &=-\frac {47 e^x}{2}+47 x-47 e^x x-47 x^2-\frac {47 e^x x^2}{2}-47 x (1-\log (5))+\frac {47}{2} e^x (1+x) \log (5)+\frac {47}{2} e^x \log (x)-47 x \log (x)-\frac {47}{2} e^x (1+x) \log (x)+\frac {47 \int e^x \, dx}{2}+47 \int e^x \, dx+47 \int e^x x \, dx-\frac {1}{2} (47 \log (5)) \int e^x \, dx\\ &=47 e^x+47 x-47 x^2-\frac {47 e^x x^2}{2}-47 x (1-\log (5))-\frac {47}{2} e^x \log (5)+\frac {47}{2} e^x (1+x) \log (5)+\frac {47}{2} e^x \log (x)-47 x \log (x)-\frac {47}{2} e^x (1+x) \log (x)-47 \int e^x \, dx\\ &=47 x-47 x^2-\frac {47 e^x x^2}{2}-47 x (1-\log (5))-\frac {47}{2} e^x \log (5)+\frac {47}{2} e^x (1+x) \log (5)+\frac {47}{2} e^x \log (x)-47 x \log (x)-\frac {47}{2} e^x (1+x) \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.04, size = 18, normalized size = 0.82 \begin {gather*} -\frac {47}{2} \left (2+e^x\right ) x \left (x+\log \left (\frac {x}{5}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.27, size = 38, normalized size = 1.73
method | result | size |
default | \(-47 x^{2}-\frac {47 x \,{\mathrm e}^{x} \ln \left (x \right )}{2}-47 x \ln \left (x \right )-\frac {47 \,{\mathrm e}^{x} x^{2}}{2}+\frac {47 x \,{\mathrm e}^{x} \ln \left (5\right )}{2}+47 x \ln \left (5\right )\) | \(38\) |
norman | \(-47 x^{2}-\frac {47 x \,{\mathrm e}^{x} \ln \left (x \right )}{2}-47 x \ln \left (x \right )-\frac {47 \,{\mathrm e}^{x} x^{2}}{2}+\frac {47 x \,{\mathrm e}^{x} \ln \left (5\right )}{2}+47 x \ln \left (5\right )\) | \(38\) |
risch | \(-47 x^{2}-\frac {47 x \,{\mathrm e}^{x} \ln \left (x \right )}{2}-47 x \ln \left (x \right )-\frac {47 \,{\mathrm e}^{x} x^{2}}{2}+\frac {47 x \,{\mathrm e}^{x} \ln \left (5\right )}{2}+47 x \ln \left (5\right )\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 41 vs.
\(2 (17) = 34\).
time = 0.49, size = 41, normalized size = 1.86 \begin {gather*} -47 \, x^{2} - \frac {47}{2} \, {\left (x^{2} - x \log \left (5\right ) + 1\right )} e^{x} + 47 \, x \log \left (5\right ) - \frac {47}{2} \, {\left (x e^{x} + 2 \, x\right )} \log \left (x\right ) + \frac {47}{2} \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 36 vs.
\(2 (17) = 34\).
time = 0.37, size = 36, normalized size = 1.64 \begin {gather*} -47 \, x^{2} - \frac {47}{2} \, {\left (x^{2} - x \log \left (5\right )\right )} e^{x} + 47 \, x \log \left (5\right ) - \frac {47}{2} \, {\left (x e^{x} + 2 \, x\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.12, size = 41, normalized size = 1.86 \begin {gather*} - 47 x^{2} - 47 x \log {\left (x \right )} + 47 x \log {\left (5 \right )} + \frac {\left (- 47 x^{2} - 47 x \log {\left (x \right )} + 47 x \log {\left (5 \right )}\right ) e^{x}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 41 vs.
\(2 (17) = 34\).
time = 0.40, size = 41, normalized size = 1.86 \begin {gather*} -47 \, x^{2} - \frac {47}{2} \, {\left (x^{2} - x \log \left (5\right ) + 1\right )} e^{x} + 47 \, x \log \left (5\right ) - \frac {47}{2} \, {\left (x e^{x} + 2 \, x\right )} \log \left (x\right ) + \frac {47}{2} \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.33, size = 13, normalized size = 0.59 \begin {gather*} -\frac {47\,x\,\left (x+\ln \left (\frac {x}{5}\right )\right )\,\left ({\mathrm {e}}^x+2\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________