Optimal. Leaf size=20 \[ 3-4 e^2 \left (-e^{4+x}+\frac {3}{x}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps
used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {14, 2225}
\begin {gather*} 4 e^{x+6}-\frac {12 e^2}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (4 e^{6+x}+\frac {12 e^2}{x^2}\right ) \, dx\\ &=-\frac {12 e^2}{x}+4 \int e^{6+x} \, dx\\ &=4 e^{6+x}-\frac {12 e^2}{x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 16, normalized size = 0.80 \begin {gather*} 4 e^2 \left (e^{4+x}-\frac {3}{x}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.43, size = 82, normalized size = 4.10
method | result | size |
risch | \(-\frac {12 \,{\mathrm e}^{2}}{x}+4 \,{\mathrm e}^{x +6}\) | \(15\) |
norman | \(\frac {4 x \,{\mathrm e}^{2} {\mathrm e}^{4+x}-12 \,{\mathrm e}^{2}}{x}\) | \(19\) |
derivativedivides | \(4 \,{\mathrm e}^{2} \left ({\mathrm e}^{4+x}-\frac {16 \,{\mathrm e}^{4+x}}{x}-24 \,{\mathrm e}^{4} \expIntegral \left (1, -x \right )\right )-\frac {12 \,{\mathrm e}^{2}}{x}+64 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{4+x}}{x}-{\mathrm e}^{4} \expIntegral \left (1, -x \right )\right )-32 \,{\mathrm e}^{2} \left (-\frac {4 \,{\mathrm e}^{4+x}}{x}-5 \,{\mathrm e}^{4} \expIntegral \left (1, -x \right )\right )\) | \(82\) |
default | \(4 \,{\mathrm e}^{2} \left ({\mathrm e}^{4+x}-\frac {16 \,{\mathrm e}^{4+x}}{x}-24 \,{\mathrm e}^{4} \expIntegral \left (1, -x \right )\right )-\frac {12 \,{\mathrm e}^{2}}{x}+64 \,{\mathrm e}^{2} \left (-\frac {{\mathrm e}^{4+x}}{x}-{\mathrm e}^{4} \expIntegral \left (1, -x \right )\right )-32 \,{\mathrm e}^{2} \left (-\frac {4 \,{\mathrm e}^{4+x}}{x}-5 \,{\mathrm e}^{4} \expIntegral \left (1, -x \right )\right )\) | \(82\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 14, normalized size = 0.70 \begin {gather*} -\frac {12 \, e^{2}}{x} + 4 \, e^{\left (x + 6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 16, normalized size = 0.80 \begin {gather*} \frac {4 \, {\left (x e^{\left (x + 6\right )} - 3 \, e^{2}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 15, normalized size = 0.75 \begin {gather*} 4 e^{2} e^{x + 4} - \frac {12 e^{2}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 16, normalized size = 0.80 \begin {gather*} \frac {4 \, {\left (x e^{\left (x + 6\right )} - 3 \, e^{2}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.06, size = 14, normalized size = 0.70 \begin {gather*} 4\,{\mathrm {e}}^6\,{\mathrm {e}}^x-\frac {12\,{\mathrm {e}}^2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________