Optimal. Leaf size=28 \[ \frac {x^3}{3}+2 e^x x-2 e^x+\frac {e^{2 x}}{2} \]
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Rubi [A] time = 0.02, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.429, Rules used = {6742, 2194, 2176} \[ \frac {x^3}{3}+2 e^x x-2 e^x+\frac {e^{2 x}}{2} \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rule 6742
Rubi steps
\begin {align*} \int \left (e^x+x\right )^2 \, dx &=\int \left (e^{2 x}+2 e^x x+x^2\right ) \, dx\\ &=\frac {x^3}{3}+2 \int e^x x \, dx+\int e^{2 x} \, dx\\ &=\frac {e^{2 x}}{2}+2 e^x x+\frac {x^3}{3}-2 \int e^x \, dx\\ &=-2 e^x+\frac {e^{2 x}}{2}+2 e^x x+\frac {x^3}{3}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 26, normalized size = 0.93 \[ \frac {x^3}{3}+\frac {e^{2 x}}{2}+e^x (2 x-2) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 19, normalized size = 0.68 \[ \frac {1}{3} \, x^{3} + 2 \, {\left (x - 1\right )} e^{x} + \frac {1}{2} \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 19, normalized size = 0.68 \[ \frac {1}{3} \, x^{3} + 2 \, {\left (x - 1\right )} e^{x} + \frac {1}{2} \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 22, normalized size = 0.79 \[ \frac {x^{3}}{3}+2 x \,{\mathrm e}^{x}-2 \,{\mathrm e}^{x}+\frac {{\mathrm e}^{2 x}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.01, size = 19, normalized size = 0.68 \[ \frac {1}{3} \, x^{3} + 2 \, {\left (x - 1\right )} e^{x} + \frac {1}{2} \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.50, size = 21, normalized size = 0.75 \[ \frac {{\mathrm {e}}^{2\,x}}{2}-2\,{\mathrm {e}}^x+2\,x\,{\mathrm {e}}^x+\frac {x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 20, normalized size = 0.71 \[ \frac {x^{3}}{3} + \frac {\left (4 x - 4\right ) e^{x}}{2} + \frac {e^{2 x}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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