Optimal. Leaf size=21 \[ -4+e^x+\left (e^x-x-\frac {23 x^2}{2}\right )^2 \]
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Rubi [A]
time = 0.05, antiderivative size = 38, normalized size of antiderivative = 1.81, number of steps
used = 10, number of rules used = 3, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {2225, 2227,
2207} \begin {gather*} \frac {529 x^4}{4}+23 x^3-23 e^x x^2+x^2-2 e^x x+e^x+e^{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x^2+23 x^3+\frac {529 x^4}{4}+2 \int e^{2 x} \, dx+\int e^x \left (-1-48 x-23 x^2\right ) \, dx\\ &=e^{2 x}+x^2+23 x^3+\frac {529 x^4}{4}+\int \left (-e^x-48 e^x x-23 e^x x^2\right ) \, dx\\ &=e^{2 x}+x^2+23 x^3+\frac {529 x^4}{4}-23 \int e^x x^2 \, dx-48 \int e^x x \, dx-\int e^x \, dx\\ &=-e^x+e^{2 x}-48 e^x x+x^2-23 e^x x^2+23 x^3+\frac {529 x^4}{4}+46 \int e^x x \, dx+48 \int e^x \, dx\\ &=47 e^x+e^{2 x}-2 e^x x+x^2-23 e^x x^2+23 x^3+\frac {529 x^4}{4}-46 \int e^x \, dx\\ &=e^x+e^{2 x}-2 e^x x+x^2-23 e^x x^2+23 x^3+\frac {529 x^4}{4}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 36, normalized size = 1.71 \begin {gather*} e^{2 x}+x^2+23 x^3+\frac {529 x^4}{4}-e^x \left (-1+2 x+23 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.27, size = 33, normalized size = 1.57
method | result | size |
risch | \({\mathrm e}^{2 x}+\left (-23 x^{2}-2 x +1\right ) {\mathrm e}^{x}+\frac {529 x^{4}}{4}+23 x^{3}+x^{2}\) | \(32\) |
default | \(-2 \,{\mathrm e}^{x} x +{\mathrm e}^{x}-23 \,{\mathrm e}^{x} x^{2}+x^{2}+23 x^{3}+\frac {529 x^{4}}{4}+{\mathrm e}^{2 x}\) | \(33\) |
norman | \(-2 \,{\mathrm e}^{x} x +{\mathrm e}^{x}-23 \,{\mathrm e}^{x} x^{2}+x^{2}+23 x^{3}+\frac {529 x^{4}}{4}+{\mathrm e}^{2 x}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 32, normalized size = 1.52 \begin {gather*} \frac {529}{4} \, x^{4} + 23 \, x^{3} + x^{2} - {\left (23 \, x^{2} + 2 \, x - 1\right )} e^{x} + e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 32, normalized size = 1.52 \begin {gather*} \frac {529}{4} \, x^{4} + 23 \, x^{3} + x^{2} - {\left (23 \, x^{2} + 2 \, x - 1\right )} e^{x} + e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 32, normalized size = 1.52 \begin {gather*} \frac {529 x^{4}}{4} + 23 x^{3} + x^{2} + \left (- 23 x^{2} - 2 x + 1\right ) e^{x} + e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 32, normalized size = 1.52 \begin {gather*} \frac {529}{4} \, x^{4} + 23 \, x^{3} + x^{2} - {\left (23 \, x^{2} + 2 \, x - 1\right )} e^{x} + e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 32, normalized size = 1.52 \begin {gather*} {\mathrm {e}}^{2\,x}+{\mathrm {e}}^x-23\,x^2\,{\mathrm {e}}^x-2\,x\,{\mathrm {e}}^x+x^2+23\,x^3+\frac {529\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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