Optimal. Leaf size=17 \[ -2 e^{-2+10 (4-12501 x)^2}+x \]
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Rubi [A] time = 0.23, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 7, number of rules used = 4, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {6742, 2234, 2204, 2240} \begin {gather*} x-2 e^{1562750010 x^2-1000080 x+158} \end {gather*}
Antiderivative was successfully verified.
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Rule 2204
Rule 2234
Rule 2240
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+2000160 e^{158-1000080 x+1562750010 x^2}-6251000040 e^{158-1000080 x+1562750010 x^2} x\right ) \, dx\\ &=x+2000160 \int e^{158-1000080 x+1562750010 x^2} \, dx-6251000040 \int e^{158-1000080 x+1562750010 x^2} x \, dx\\ &=-2 e^{158-1000080 x+1562750010 x^2}+x-2000160 \int e^{158-1000080 x+1562750010 x^2} \, dx+\frac {2000160 \int e^{\frac {(-1000080+3125500020 x)^2}{6251000040}} \, dx}{e^2}\\ &=-2 e^{158-1000080 x+1562750010 x^2}+x-\frac {8 \sqrt {10 \pi } \text {erfi}\left (\sqrt {10} (4-12501 x)\right )}{e^2}-\frac {2000160 \int e^{\frac {(-1000080+3125500020 x)^2}{6251000040}} \, dx}{e^2}\\ &=-2 e^{158-1000080 x+1562750010 x^2}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 16, normalized size = 0.94 \begin {gather*} -2 e^{158-1000080 x+1562750010 x^2}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 15, normalized size = 0.88 \begin {gather*} x - 2 \, e^{\left (1562750010 \, x^{2} - 1000080 \, x + 158\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 0.94
method | result | size |
default | \(x -2 \,{\mathrm e}^{1562750010 x^{2}-1000080 x +158}\) | \(16\) |
risch | \(x -2 \,{\mathrm e}^{1562750010 x^{2}-1000080 x +158}\) | \(16\) |
norman | \(\left (-2+x \,{\mathrm e}^{-1562750010 x^{2}+1000080 x -158}\right ) {\mathrm e}^{1562750010 x^{2}-1000080 x +158}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.79, size = 86, normalized size = 5.06 \begin {gather*} -8 i \, \sqrt {10} \sqrt {\pi } \operatorname {erf}\left (12501 i \, \sqrt {10} x - 4 i \, \sqrt {10}\right ) e^{\left (-2\right )} - \frac {1}{5} \, \sqrt {10} {\left (\frac {40 \, \sqrt {\pi } {\left (12501 \, x - 4\right )} {\left (\operatorname {erf}\left (\sqrt {10} \sqrt {-{\left (12501 \, x - 4\right )}^{2}}\right ) - 1\right )}}{\sqrt {-{\left (12501 \, x - 4\right )}^{2}}} + \sqrt {10} e^{\left (10 \, {\left (12501 \, x - 4\right )}^{2}\right )}\right )} e^{\left (-2\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 16, normalized size = 0.94 \begin {gather*} x-2\,{\mathrm {e}}^{-1000080\,x}\,{\mathrm {e}}^{158}\,{\mathrm {e}}^{1562750010\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 14, normalized size = 0.82 \begin {gather*} x - 2 e^{1562750010 x^{2} - 1000080 x + 158} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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