Optimal. Leaf size=19 \[ e^x x^2-7 e^x x+7 e^x \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 4, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.364, Rules used = {1593, 2196, 2176, 2194} \[ e^x x^2-7 e^x x+7 e^x \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1593
Rule 2176
Rule 2194
Rule 2196
Rubi steps
\begin {align*} \int e^x \left (-5 x+x^2\right ) \, dx &=\int e^x (-5+x) x \, dx\\ &=\int \left (-5 e^x x+e^x x^2\right ) \, dx\\ &=-\left (5 \int e^x x \, dx\right )+\int e^x x^2 \, dx\\ &=-5 e^x x+e^x x^2-2 \int e^x x \, dx+5 \int e^x \, dx\\ &=5 e^x-7 e^x x+e^x x^2+2 \int e^x \, dx\\ &=7 e^x-7 e^x x+e^x x^2\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 12, normalized size = 0.63 \[ e^x \left (x^2-7 x+7\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.38, size = 11, normalized size = 0.58 \[ {\left (x^{2} - 7 \, x + 7\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 11, normalized size = 0.58 \[ {\left (x^{2} - 7 \, x + 7\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 12, normalized size = 0.63 \[ \left (x^{2}-7 x +7\right ) {\mathrm e}^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.97, size = 19, normalized size = 1.00 \[ {\left (x^{2} - 2 \, x + 2\right )} e^{x} - 5 \, {\left (x - 1\right )} e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.46, size = 11, normalized size = 0.58 \[ {\mathrm {e}}^x\,\left (x^2-7\,x+7\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 10, normalized size = 0.53 \[ \left (x^{2} - 7 x + 7\right ) e^{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________