Optimal. Leaf size=51 \[ e^x x^6-7 e^x x^5+36 e^x x^4-145 e^x x^3+435 e^x x^2-870 e^x x+871 e^x \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.171166, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 25, number of rules used = 3, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.136, Rules used = {2196, 2194, 2176} \[ e^x x^6-7 e^x x^5+36 e^x x^4-145 e^x x^3+435 e^x x^2-870 e^x x+871 e^x \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2196
Rule 2194
Rule 2176
Rubi steps
\begin{align*} \int e^x \left (1-x^3+x^4-x^5+x^6\right ) \, dx &=\int \left (e^x-e^x x^3+e^x x^4-e^x x^5+e^x x^6\right ) \, dx\\ &=\int e^x \, dx-\int e^x x^3 \, dx+\int e^x x^4 \, dx-\int e^x x^5 \, dx+\int e^x x^6 \, dx\\ &=e^x-e^x x^3+e^x x^4-e^x x^5+e^x x^6+3 \int e^x x^2 \, dx-4 \int e^x x^3 \, dx+5 \int e^x x^4 \, dx-6 \int e^x x^5 \, dx\\ &=e^x+3 e^x x^2-5 e^x x^3+6 e^x x^4-7 e^x x^5+e^x x^6-6 \int e^x x \, dx+12 \int e^x x^2 \, dx-20 \int e^x x^3 \, dx+30 \int e^x x^4 \, dx\\ &=e^x-6 e^x x+15 e^x x^2-25 e^x x^3+36 e^x x^4-7 e^x x^5+e^x x^6+6 \int e^x \, dx-24 \int e^x x \, dx+60 \int e^x x^2 \, dx-120 \int e^x x^3 \, dx\\ &=7 e^x-30 e^x x+75 e^x x^2-145 e^x x^3+36 e^x x^4-7 e^x x^5+e^x x^6+24 \int e^x \, dx-120 \int e^x x \, dx+360 \int e^x x^2 \, dx\\ &=31 e^x-150 e^x x+435 e^x x^2-145 e^x x^3+36 e^x x^4-7 e^x x^5+e^x x^6+120 \int e^x \, dx-720 \int e^x x \, dx\\ &=151 e^x-870 e^x x+435 e^x x^2-145 e^x x^3+36 e^x x^4-7 e^x x^5+e^x x^6+720 \int e^x \, dx\\ &=871 e^x-870 e^x x+435 e^x x^2-145 e^x x^3+36 e^x x^4-7 e^x x^5+e^x x^6\\ \end{align*}
Mathematica [A] time = 0.0248788, size = 32, normalized size = 0.63 \[ e^x \left (x^6-7 x^5+36 x^4-145 x^3+435 x^2-870 x+871\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 32, normalized size = 0.6 \begin{align*} \left ({x}^{6}-7\,{x}^{5}+36\,{x}^{4}-145\,{x}^{3}+435\,{x}^{2}-870\,x+871 \right ){{\rm e}^{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] time = 0.939958, size = 134, normalized size = 2.63 \begin{align*}{\left (x^{6} - 6 \, x^{5} + 30 \, x^{4} - 120 \, x^{3} + 360 \, x^{2} - 720 \, x + 720\right )} e^{x} -{\left (x^{5} - 5 \, x^{4} + 20 \, x^{3} - 60 \, x^{2} + 120 \, x - 120\right )} e^{x} +{\left (x^{4} - 4 \, x^{3} + 12 \, x^{2} - 24 \, x + 24\right )} e^{x} -{\left (x^{3} - 3 \, x^{2} + 6 \, x - 6\right )} e^{x} + e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.5627, size = 84, normalized size = 1.65 \begin{align*}{\left (x^{6} - 7 \, x^{5} + 36 \, x^{4} - 145 \, x^{3} + 435 \, x^{2} - 870 \, x + 871\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.094271, size = 31, normalized size = 0.61 \begin{align*} \left (x^{6} - 7 x^{5} + 36 x^{4} - 145 x^{3} + 435 x^{2} - 870 x + 871\right ) e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.07739, size = 42, normalized size = 0.82 \begin{align*}{\left (x^{6} - 7 \, x^{5} + 36 \, x^{4} - 145 \, x^{3} + 435 \, x^{2} - 870 \, x + 871\right )} e^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]