Optimal. Leaf size=28 \[ 3 \left (-4-e^{-5+\frac {9 (5-x)}{x^2}}+e^{2-2 x}+x\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.50, antiderivative size = 29, normalized size of antiderivative = 1.04, number of steps used = 7, number of rules used = 5, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 14, 2194, 6688, 6706} \begin {gather*} -3 e^{\frac {9 (5-x)}{x^2}-5}+3 x+3 e^{2-2 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 2194
Rule 6688
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{\frac {45-9 x}{x^2}} (270-27 x)+3 e^5 x^3-6 e^{7-2 x} x^3}{x^3} \, dx}{e^5}\\ &=\frac {\int \left (-6 e^{7-2 x}+\frac {3 e^{-9/x} \left (90 e^{\frac {45}{x^2}}-9 e^{\frac {45}{x^2}} x+e^{5+\frac {9}{x}} x^3\right )}{x^3}\right ) \, dx}{e^5}\\ &=\frac {3 \int \frac {e^{-9/x} \left (90 e^{\frac {45}{x^2}}-9 e^{\frac {45}{x^2}} x+e^{5+\frac {9}{x}} x^3\right )}{x^3} \, dx}{e^5}-\frac {6 \int e^{7-2 x} \, dx}{e^5}\\ &=3 e^{2-2 x}+\frac {3 \int \left (e^5-\frac {9 e^{-\frac {9 (-5+x)}{x^2}} (-10+x)}{x^3}\right ) \, dx}{e^5}\\ &=3 e^{2-2 x}+3 x-\frac {27 \int \frac {e^{-\frac {9 (-5+x)}{x^2}} (-10+x)}{x^3} \, dx}{e^5}\\ &=-3 e^{-5+\frac {9 (5-x)}{x^2}}+3 e^{2-2 x}+3 x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.09, size = 29, normalized size = 1.04 \begin {gather*} -3 e^{-5+\frac {45}{x^2}-\frac {9}{x}}+3 e^{2-2 x}+3 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.54, size = 26, normalized size = 0.93 \begin {gather*} 3 \, {\left (x e^{5} + e^{\left (-2 \, x + 7\right )} - e^{\left (-\frac {9 \, {\left (x - 5\right )}}{x^{2}}\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.18, size = 29, normalized size = 1.04 \begin {gather*} 3 \, {\left (x e^{5} + e^{\left (-2 \, x + 7\right )} - e^{\left (-\frac {9}{x} + \frac {45}{x^{2}}\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 31, normalized size = 1.11
method | result | size |
risch | \(3 x +3 \,{\mathrm e}^{-2 x +2}-3 \,{\mathrm e}^{-\frac {5 x^{2}+9 x -45}{x^{2}}}\) | \(31\) |
default | \({\mathrm e}^{-5} \left (-3 \,{\mathrm e}^{-\frac {9}{x}+\frac {45}{x^{2}}}+3 \,{\mathrm e}^{5} {\mathrm e}^{-2 x} {\mathrm e}^{2}+3 x \,{\mathrm e}^{5}\right )\) | \(36\) |
norman | \(\frac {3 x^{3}+3 x^{2} {\mathrm e}^{-2 x +2}-3 x^{2} {\mathrm e}^{-5} {\mathrm e}^{\frac {-9 x +45}{x^{2}}}}{x^{2}}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.42, size = 42, normalized size = 1.50 \begin {gather*} 3 \, {\left (x e^{5} - {\left (e^{\left (2 \, x + \frac {45}{x^{2}}\right )} - e^{\left (\frac {9}{x} + 7\right )}\right )} e^{\left (-2 \, x - \frac {9}{x}\right )}\right )} e^{\left (-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 7.86, size = 28, normalized size = 1.00 \begin {gather*} 3\,x+3\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^2-3\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^{-\frac {9}{x}}\,{\mathrm {e}}^{\frac {45}{x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.37, size = 26, normalized size = 0.93 \begin {gather*} 3 x - \frac {3 e^{\frac {45 - 9 x}{x^{2}}}}{e^{5}} + 3 e^{2 - 2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________