Optimal. Leaf size=17 \[ 1+\left (x+x^4\right )^2+\frac {x}{\log (10+x)} \]
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Rubi [A]
time = 0.13, antiderivative size = 30, normalized size of antiderivative = 1.76, number of steps
used = 13, number of rules used = 9, integrand size = 60, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {6820, 14,
2458, 2395, 2334, 2335, 2339, 30, 2436} \begin {gather*} x^8+2 x^5+x^2+\frac {x+10}{\log (x+10)}-\frac {10}{\log (x+10)} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 30
Rule 2334
Rule 2335
Rule 2339
Rule 2395
Rule 2436
Rule 2458
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2 x \left (1+5 x^3+4 x^6\right )-\frac {x}{(10+x) \log ^2(10+x)}+\frac {1}{\log (10+x)}\right ) \, dx\\ &=2 \int x \left (1+5 x^3+4 x^6\right ) \, dx-\int \frac {x}{(10+x) \log ^2(10+x)} \, dx+\int \frac {1}{\log (10+x)} \, dx\\ &=2 \int \left (x+5 x^4+4 x^7\right ) \, dx-\text {Subst}\left (\int \frac {-10+x}{x \log ^2(x)} \, dx,x,10+x\right )+\text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,10+x\right )\\ &=x^2+2 x^5+x^8+\text {li}(10+x)-\text {Subst}\left (\int \left (\frac {1}{\log ^2(x)}-\frac {10}{x \log ^2(x)}\right ) \, dx,x,10+x\right )\\ &=x^2+2 x^5+x^8+\text {li}(10+x)+10 \text {Subst}\left (\int \frac {1}{x \log ^2(x)} \, dx,x,10+x\right )-\text {Subst}\left (\int \frac {1}{\log ^2(x)} \, dx,x,10+x\right )\\ &=x^2+2 x^5+x^8+\frac {10+x}{\log (10+x)}+\text {li}(10+x)+10 \text {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (10+x)\right )-\text {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,10+x\right )\\ &=x^2+2 x^5+x^8-\frac {10}{\log (10+x)}+\frac {10+x}{\log (10+x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 18, normalized size = 1.06 \begin {gather*} x \left (x \left (1+x^3\right )^2+\frac {1}{\log (10+x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(70\) vs.
\(2(17)=34\).
time = 0.35, size = 71, normalized size = 4.18
method | result | size |
risch | \(x^{8}+2 x^{5}+x^{2}+\frac {x}{\ln \left (x +10\right )}\) | \(21\) |
derivativedivides | \(\left (x +10\right )^{8}-80 \left (x +10\right )^{7}+2800 \left (x +10\right )^{6}-55998 \left (x +10\right )^{5}+699900 \left (x +10\right )^{4}-5598000 \left (x +10\right )^{3}+27980001 \left (x +10\right )^{2}-79900020 x -799000200+\frac {x +10}{\ln \left (x +10\right )}-\frac {10}{\ln \left (x +10\right )}\) | \(71\) |
default | \(\left (x +10\right )^{8}-80 \left (x +10\right )^{7}+2800 \left (x +10\right )^{6}-55998 \left (x +10\right )^{5}+699900 \left (x +10\right )^{4}-5598000 \left (x +10\right )^{3}+27980001 \left (x +10\right )^{2}-79900020 x -799000200+\frac {x +10}{\ln \left (x +10\right )}-\frac {10}{\ln \left (x +10\right )}\) | \(71\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 26, normalized size = 1.53 \begin {gather*} \frac {{\left (x^{8} + 2 \, x^{5} + x^{2}\right )} \log \left (x + 10\right ) + x}{\log \left (x + 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 26, normalized size = 1.53 \begin {gather*} \frac {{\left (x^{8} + 2 \, x^{5} + x^{2}\right )} \log \left (x + 10\right ) + x}{\log \left (x + 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 17, normalized size = 1.00 \begin {gather*} x^{8} + 2 x^{5} + x^{2} + \frac {x}{\log {\left (x + 10 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 20, normalized size = 1.18 \begin {gather*} x^{8} + 2 \, x^{5} + x^{2} + \frac {x}{\log \left (x + 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.46, size = 20, normalized size = 1.18 \begin {gather*} \frac {x}{\ln \left (x+10\right )}+x^2+2\,x^5+x^8 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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