Optimal. Leaf size=15 \[ e^{5-9 e^{10}+x} x (5+x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.08, antiderivative size = 28, normalized size of antiderivative = 1.87, number of steps
used = 8, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {2227, 2225,
2207} \begin {gather*} e^{x-9 e^{10}+5} x^2+5 e^{x-9 e^{10}+5} x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2207
Rule 2225
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (5 e^{5-9 e^{10}+x}+7 e^{5-9 e^{10}+x} x+e^{5-9 e^{10}+x} x^2\right ) \, dx\\ &=5 \int e^{5-9 e^{10}+x} \, dx+7 \int e^{5-9 e^{10}+x} x \, dx+\int e^{5-9 e^{10}+x} x^2 \, dx\\ &=5 e^{5-9 e^{10}+x}+7 e^{5-9 e^{10}+x} x+e^{5-9 e^{10}+x} x^2-2 \int e^{5-9 e^{10}+x} x \, dx-7 \int e^{5-9 e^{10}+x} \, dx\\ &=-2 e^{5-9 e^{10}+x}+5 e^{5-9 e^{10}+x} x+e^{5-9 e^{10}+x} x^2+2 \int e^{5-9 e^{10}+x} \, dx\\ &=5 e^{5-9 e^{10}+x} x+e^{5-9 e^{10}+x} x^2\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.04, size = 15, normalized size = 1.00 \begin {gather*} e^{5-9 e^{10}+x} x (5+x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(115\) vs.
\(2(15)=30\).
time = 0.37, size = 116, normalized size = 7.73
method | result | size |
gosper | \(\left (5+x \right ) x \,{\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x}\) | \(16\) |
risch | \(\left (x^{2}+5 x \right ) {\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x}\) | \(17\) |
norman | \(x^{2} {\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x}+5 x \,{\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x}\) | \(29\) |
meijerg | \(-{\mathrm e}^{-9 \,{\mathrm e}^{10}+5} \left (2-\frac {\left (3 x^{2}-6 x +6\right ) {\mathrm e}^{x}}{3}\right )+7 \,{\mathrm e}^{-9 \,{\mathrm e}^{10}+5} \left (1-\frac {\left (-2 x +2\right ) {\mathrm e}^{x}}{2}\right )-5 \,{\mathrm e}^{-9 \,{\mathrm e}^{10}+5} \left (1-{\mathrm e}^{x}\right )\) | \(62\) |
derivativedivides | \({\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x} \left (-9 \,{\mathrm e}^{10}+5+x \right )^{2}-5 \,{\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x} \left (-9 \,{\mathrm e}^{10}+5+x \right )-27 \,{\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x} {\mathrm e}^{10}+81 \,{\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x} {\mathrm e}^{20}+18 \,{\mathrm e}^{10} \left ({\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x} \left (-9 \,{\mathrm e}^{10}+5+x \right )-{\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x}\right )\) | \(116\) |
default | \({\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x} \left (-9 \,{\mathrm e}^{10}+5+x \right )^{2}-5 \,{\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x} \left (-9 \,{\mathrm e}^{10}+5+x \right )-27 \,{\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x} {\mathrm e}^{10}+81 \,{\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x} {\mathrm e}^{20}+18 \,{\mathrm e}^{10} \left ({\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x} \left (-9 \,{\mathrm e}^{10}+5+x \right )-{\mathrm e}^{-9 \,{\mathrm e}^{10}+5+x}\right )\) | \(116\) |
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. 53 vs.
\(2 (13) = 26\).
time = 0.27, size = 53, normalized size = 3.53 \begin {gather*} {\left (x^{2} e^{5} - 2 \, x e^{5} + 2 \, e^{5}\right )} e^{\left (x - 9 \, e^{10}\right )} + 7 \, {\left (x e^{5} - e^{5}\right )} e^{\left (x - 9 \, e^{10}\right )} + 5 \, e^{\left (x - 9 \, e^{10} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.40, size = 16, normalized size = 1.07 \begin {gather*} {\left (x^{2} + 5 \, x\right )} e^{\left (x - 9 \, e^{10} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 15, normalized size = 1.00 \begin {gather*} \left (x^{2} + 5 x\right ) e^{x - 9 e^{10} + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 16, normalized size = 1.07 \begin {gather*} {\left (x^{2} + 5 \, x\right )} e^{\left (x - 9 \, e^{10} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.01, size = 14, normalized size = 0.93 \begin {gather*} x\,{\mathrm {e}}^{-9\,{\mathrm {e}}^{10}}\,{\mathrm {e}}^5\,{\mathrm {e}}^x\,\left (x+5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________