Optimal. Leaf size=22 \[ x+x \left (-4-x^6+\frac {20 \left (e^x+x\right )}{\log (25)}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 39, normalized size of antiderivative = 1.77, number of steps
used = 5, number of rules used = 3, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.107, Rules used = {12, 2207, 2225}
\begin {gather*} -x^7+\frac {20 x^2}{\log (25)}-3 x-\frac {20 e^x}{\log (25)}+\frac {20 e^x (x+1)}{\log (25)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (40 x+e^x (20+20 x)+\left (-3-7 x^6\right ) \log (25)\right ) \, dx}{\log (25)}\\ &=\frac {20 x^2}{\log (25)}+\frac {\int e^x (20+20 x) \, dx}{\log (25)}+\int \left (-3-7 x^6\right ) \, dx\\ &=-3 x-x^7+\frac {20 x^2}{\log (25)}+\frac {20 e^x (1+x)}{\log (25)}-\frac {20 \int e^x \, dx}{\log (25)}\\ &=-3 x-x^7-\frac {20 e^x}{\log (25)}+\frac {20 x^2}{\log (25)}+\frac {20 e^x (1+x)}{\log (25)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 29, normalized size = 1.32 \begin {gather*} \frac {20 e^x x+20 x^2-3 x \log (25)-x^7 \log (25)}{\log (25)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.28, size = 30, normalized size = 1.36
method | result | size |
norman | \(-3 x -x^{7}+\frac {10 x^{2}}{\ln \left (5\right )}+\frac {10 \,{\mathrm e}^{x} x}{\ln \left (5\right )}\) | \(28\) |
risch | \(-3 x -x^{7}+\frac {10 x^{2}}{\ln \left (5\right )}+\frac {10 \,{\mathrm e}^{x} x}{\ln \left (5\right )}\) | \(28\) |
default | \(\frac {20 \,{\mathrm e}^{x} x +20 x^{2}-2 x^{7} \ln \left (5\right )-6 x \ln \left (5\right )}{2 \ln \left (5\right )}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.36, size = 27, normalized size = 1.23 \begin {gather*} \frac {10 \, x^{2} + 10 \, x e^{x} - {\left (x^{7} + 3 \, x\right )} \log \left (5\right )}{\log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 27, normalized size = 1.23 \begin {gather*} \frac {10 \, x^{2} + 10 \, x e^{x} - {\left (x^{7} + 3 \, x\right )} \log \left (5\right )}{\log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 24, normalized size = 1.09 \begin {gather*} - x^{7} + \frac {10 x^{2}}{\log {\left (5 \right )}} + \frac {10 x e^{x}}{\log {\left (5 \right )}} - 3 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 27, normalized size = 1.23 \begin {gather*} \frac {10 \, x^{2} + 10 \, x e^{x} - {\left (x^{7} + 3 \, x\right )} \log \left (5\right )}{\log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 25, normalized size = 1.14 \begin {gather*} \frac {x\,\left (10\,x-3\,\ln \left (5\right )+10\,{\mathrm {e}}^x-x^6\,\ln \left (5\right )\right )}{\ln \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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