Optimal. Leaf size=17 \[ 75 (2+x) \left (2+e^{3 x^2}+x^2\right ) \]
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Rubi [A]
time = 0.07, antiderivative size = 33, normalized size of antiderivative = 1.94, number of steps
used = 7, number of rules used = 4, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2258, 2235,
2240, 2243} \begin {gather*} 75 x^3+150 x^2+75 e^{3 x^2} x+150 e^{3 x^2}+150 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2235
Rule 2240
Rule 2243
Rule 2258
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=150 x+150 x^2+75 x^3+\int e^{3 x^2} \left (75+900 x+450 x^2\right ) \, dx\\ &=150 x+150 x^2+75 x^3+\int \left (75 e^{3 x^2}+900 e^{3 x^2} x+450 e^{3 x^2} x^2\right ) \, dx\\ &=150 x+150 x^2+75 x^3+75 \int e^{3 x^2} \, dx+450 \int e^{3 x^2} x^2 \, dx+900 \int e^{3 x^2} x \, dx\\ &=150 e^{3 x^2}+150 x+75 e^{3 x^2} x+150 x^2+75 x^3+\frac {25}{2} \sqrt {3 \pi } \text {erfi}\left (\sqrt {3} x\right )-75 \int e^{3 x^2} \, dx\\ &=150 e^{3 x^2}+150 x+75 e^{3 x^2} x+150 x^2+75 x^3\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 32, normalized size = 1.88 \begin {gather*} 75 \left (2 e^{3 x^2}+2 x+e^{3 x^2} x+2 x^2+x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.22, size = 32, normalized size = 1.88
method | result | size |
risch | \(\left (150+75 x \right ) {\mathrm e}^{3 x^{2}}+75 x^{3}+150 x^{2}+150 x\) | \(27\) |
default | \(150 x +150 x^{2}+75 x^{3}+75 x \,{\mathrm e}^{3 x^{2}}+150 \,{\mathrm e}^{3 x^{2}}\) | \(32\) |
norman | \(150 x +150 x^{2}+75 x^{3}+75 x \,{\mathrm e}^{3 x^{2}}+150 \,{\mathrm e}^{3 x^{2}}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 25, normalized size = 1.47 \begin {gather*} 75 \, x^{3} + 150 \, x^{2} + 75 \, {\left (x + 2\right )} e^{\left (3 \, x^{2}\right )} + 150 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.51, size = 25, normalized size = 1.47 \begin {gather*} 75 \, x^{3} + 150 \, x^{2} + 75 \, {\left (x + 2\right )} e^{\left (3 \, x^{2}\right )} + 150 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 24, normalized size = 1.41 \begin {gather*} 75 x^{3} + 150 x^{2} + 150 x + \left (75 x + 150\right ) e^{3 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.45, size = 25, normalized size = 1.47 \begin {gather*} 75 \, x^{3} + 150 \, x^{2} + 75 \, {\left (x + 2\right )} e^{\left (3 \, x^{2}\right )} + 150 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.34, size = 31, normalized size = 1.82 \begin {gather*} 150\,x+150\,{\mathrm {e}}^{3\,x^2}+75\,x\,{\mathrm {e}}^{3\,x^2}+150\,x^2+75\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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