3.101.40 \(\int \frac {e^{\frac {81 x^2}{625-500 x+150 x^2-20 x^3+x^4+(50 x-20 x^2+2 x^3) \log (2+4 x)+x^2 \log ^2(2+4 x)}} (4050 x+8100 x^2-486 x^3-324 x^4)}{46875+37500 x-84375 x^2+48750 x^3-13875 x^4+2160 x^5-177 x^6+6 x^7+(5625 x+6750 x^2-7650 x^3+2520 x^4-351 x^5+18 x^6) \log (2+4 x)+(225 x^2+360 x^3-171 x^4+18 x^5) \log ^2(2+4 x)+(3 x^3+6 x^4) \log ^3(2+4 x)+e^{\frac {81 x^2}{625-500 x+150 x^2-20 x^3+x^4+(50 x-20 x^2+2 x^3) \log (2+4 x)+x^2 \log ^2(2+4 x)}} (15625+12500 x-28125 x^2+16250 x^3-4625 x^4+720 x^5-59 x^6+2 x^7+(1875 x+2250 x^2-2550 x^3+840 x^4-117 x^5+6 x^6) \log (2+4 x)+(75 x^2+120 x^3-57 x^4+6 x^5) \log ^2(2+4 x)+(x^3+2 x^4) \log ^3(2+4 x))} \, dx\)
Optimal. Leaf size=28 \[ \log \left (3+e^{\frac {81 x^2}{\left ((5-x)^2+x \log (2+4 x)\right )^2}}\right ) \]
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Rubi [A] time = 5.77, antiderivative size = 26, normalized size of antiderivative = 0.93,
number of steps used = 3, number of rules used = 3, integrand size = 383, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used
= {6688, 12, 6684} \begin {gather*} \log \left (e^{\frac {81 x^2}{\left ((x-5)^2+x \log (4 x+2)\right )^2}}+3\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Int[(E^((81*x^2)/(625 - 500*x + 150*x^2 - 20*x^3 + x^4 + (50*x - 20*x^2 + 2*x^3)*Log[2 + 4*x] + x^2*Log[2 + 4*
x]^2))*(4050*x + 8100*x^2 - 486*x^3 - 324*x^4))/(46875 + 37500*x - 84375*x^2 + 48750*x^3 - 13875*x^4 + 2160*x^
5 - 177*x^6 + 6*x^7 + (5625*x + 6750*x^2 - 7650*x^3 + 2520*x^4 - 351*x^5 + 18*x^6)*Log[2 + 4*x] + (225*x^2 + 3
60*x^3 - 171*x^4 + 18*x^5)*Log[2 + 4*x]^2 + (3*x^3 + 6*x^4)*Log[2 + 4*x]^3 + E^((81*x^2)/(625 - 500*x + 150*x^
2 - 20*x^3 + x^4 + (50*x - 20*x^2 + 2*x^3)*Log[2 + 4*x] + x^2*Log[2 + 4*x]^2))*(15625 + 12500*x - 28125*x^2 +
16250*x^3 - 4625*x^4 + 720*x^5 - 59*x^6 + 2*x^7 + (1875*x + 2250*x^2 - 2550*x^3 + 840*x^4 - 117*x^5 + 6*x^6)*L
og[2 + 4*x] + (75*x^2 + 120*x^3 - 57*x^4 + 6*x^5)*Log[2 + 4*x]^2 + (x^3 + 2*x^4)*Log[2 + 4*x]^3)),x]
[Out]
Log[3 + E^((81*x^2)/((-5 + x)^2 + x*Log[2 + 4*x])^2)]
Rule 12
Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] && !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]
Rule 6684
Int[(u_)/(y_), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Simp[q*Log[RemoveContent[y, x]], x] /; !Fa
lseQ[q]]
Rule 6688
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {162 e^{\frac {81 x^2}{\left ((-5+x)^2+x \log (2+4 x)\right )^2}} x \left (25+50 x-3 x^2-2 x^3\right )}{\left (3+e^{\frac {81 x^2}{\left ((-5+x)^2+x \log (2+4 x)\right )^2}}\right ) (1+2 x) \left ((-5+x)^2+x \log (2+4 x)\right )^3} \, dx\\ &=162 \int \frac {e^{\frac {81 x^2}{\left ((-5+x)^2+x \log (2+4 x)\right )^2}} x \left (25+50 x-3 x^2-2 x^3\right )}{\left (3+e^{\frac {81 x^2}{\left ((-5+x)^2+x \log (2+4 x)\right )^2}}\right ) (1+2 x) \left ((-5+x)^2+x \log (2+4 x)\right )^3} \, dx\\ &=\log \left (3+e^{\frac {81 x^2}{\left ((-5+x)^2+x \log (2+4 x)\right )^2}}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 26, normalized size = 0.93 \begin {gather*} \log \left (3+e^{\frac {81 x^2}{\left ((-5+x)^2+x \log (2+4 x)\right )^2}}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(E^((81*x^2)/(625 - 500*x + 150*x^2 - 20*x^3 + x^4 + (50*x - 20*x^2 + 2*x^3)*Log[2 + 4*x] + x^2*Log[
2 + 4*x]^2))*(4050*x + 8100*x^2 - 486*x^3 - 324*x^4))/(46875 + 37500*x - 84375*x^2 + 48750*x^3 - 13875*x^4 + 2
160*x^5 - 177*x^6 + 6*x^7 + (5625*x + 6750*x^2 - 7650*x^3 + 2520*x^4 - 351*x^5 + 18*x^6)*Log[2 + 4*x] + (225*x
^2 + 360*x^3 - 171*x^4 + 18*x^5)*Log[2 + 4*x]^2 + (3*x^3 + 6*x^4)*Log[2 + 4*x]^3 + E^((81*x^2)/(625 - 500*x +
150*x^2 - 20*x^3 + x^4 + (50*x - 20*x^2 + 2*x^3)*Log[2 + 4*x] + x^2*Log[2 + 4*x]^2))*(15625 + 12500*x - 28125*
x^2 + 16250*x^3 - 4625*x^4 + 720*x^5 - 59*x^6 + 2*x^7 + (1875*x + 2250*x^2 - 2550*x^3 + 840*x^4 - 117*x^5 + 6*
x^6)*Log[2 + 4*x] + (75*x^2 + 120*x^3 - 57*x^4 + 6*x^5)*Log[2 + 4*x]^2 + (x^3 + 2*x^4)*Log[2 + 4*x]^3)),x]
[Out]
Log[3 + E^((81*x^2)/((-5 + x)^2 + x*Log[2 + 4*x])^2)]
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fricas [B] time = 0.80, size = 61, normalized size = 2.18 \begin {gather*} \log \left (e^{\left (\frac {81 \, x^{2}}{x^{4} + x^{2} \log \left (4 \, x + 2\right )^{2} - 20 \, x^{3} + 150 \, x^{2} + 2 \, {\left (x^{3} - 10 \, x^{2} + 25 \, x\right )} \log \left (4 \, x + 2\right ) - 500 \, x + 625}\right )} + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-324*x^4-486*x^3+8100*x^2+4050*x)*exp(81*x^2/(x^2*log(4*x+2)^2+(2*x^3-20*x^2+50*x)*log(4*x+2)+x^4-2
0*x^3+150*x^2-500*x+625))/(((2*x^4+x^3)*log(4*x+2)^3+(6*x^5-57*x^4+120*x^3+75*x^2)*log(4*x+2)^2+(6*x^6-117*x^5
+840*x^4-2550*x^3+2250*x^2+1875*x)*log(4*x+2)+2*x^7-59*x^6+720*x^5-4625*x^4+16250*x^3-28125*x^2+12500*x+15625)
*exp(81*x^2/(x^2*log(4*x+2)^2+(2*x^3-20*x^2+50*x)*log(4*x+2)+x^4-20*x^3+150*x^2-500*x+625))+(6*x^4+3*x^3)*log(
4*x+2)^3+(18*x^5-171*x^4+360*x^3+225*x^2)*log(4*x+2)^2+(18*x^6-351*x^5+2520*x^4-7650*x^3+6750*x^2+5625*x)*log(
4*x+2)+6*x^7-177*x^6+2160*x^5-13875*x^4+48750*x^3-84375*x^2+37500*x+46875),x, algorithm="fricas")
[Out]
log(e^(81*x^2/(x^4 + x^2*log(4*x + 2)^2 - 20*x^3 + 150*x^2 + 2*(x^3 - 10*x^2 + 25*x)*log(4*x + 2) - 500*x + 62
5)) + 3)
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giac [B] time = 39.04, size = 72, normalized size = 2.57 \begin {gather*} \log \left (e^{\left (\frac {81 \, x^{2}}{x^{4} + 2 \, x^{3} \log \left (4 \, x + 2\right ) + x^{2} \log \left (4 \, x + 2\right )^{2} - 20 \, x^{3} - 20 \, x^{2} \log \left (4 \, x + 2\right ) + 150 \, x^{2} + 50 \, x \log \left (4 \, x + 2\right ) - 500 \, x + 625}\right )} + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-324*x^4-486*x^3+8100*x^2+4050*x)*exp(81*x^2/(x^2*log(4*x+2)^2+(2*x^3-20*x^2+50*x)*log(4*x+2)+x^4-2
0*x^3+150*x^2-500*x+625))/(((2*x^4+x^3)*log(4*x+2)^3+(6*x^5-57*x^4+120*x^3+75*x^2)*log(4*x+2)^2+(6*x^6-117*x^5
+840*x^4-2550*x^3+2250*x^2+1875*x)*log(4*x+2)+2*x^7-59*x^6+720*x^5-4625*x^4+16250*x^3-28125*x^2+12500*x+15625)
*exp(81*x^2/(x^2*log(4*x+2)^2+(2*x^3-20*x^2+50*x)*log(4*x+2)+x^4-20*x^3+150*x^2-500*x+625))+(6*x^4+3*x^3)*log(
4*x+2)^3+(18*x^5-171*x^4+360*x^3+225*x^2)*log(4*x+2)^2+(18*x^6-351*x^5+2520*x^4-7650*x^3+6750*x^2+5625*x)*log(
4*x+2)+6*x^7-177*x^6+2160*x^5-13875*x^4+48750*x^3-84375*x^2+37500*x+46875),x, algorithm="giac")
[Out]
log(e^(81*x^2/(x^4 + 2*x^3*log(4*x + 2) + x^2*log(4*x + 2)^2 - 20*x^3 - 20*x^2*log(4*x + 2) + 150*x^2 + 50*x*l
og(4*x + 2) - 500*x + 625)) + 3)
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maple [B] time = 0.10, size = 110, normalized size = 3.93
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result |
size |
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| risch |
\(\frac {81 x^{2}}{\left (\ln \left (4 x +2\right ) x +x^{2}-10 x +25\right )^{2}}-\frac {81 x^{2}}{x^{2} \ln \left (4 x +2\right )^{2}+\left (2 x^{3}-20 x^{2}+50 x \right ) \ln \left (4 x +2\right )+x^{4}-20 x^{3}+150 x^{2}-500 x +625}+\ln \left ({\mathrm e}^{\frac {81 x^{2}}{\left (\ln \left (4 x +2\right ) x +x^{2}-10 x +25\right )^{2}}}+3\right )\) |
\(110\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((-324*x^4-486*x^3+8100*x^2+4050*x)*exp(81*x^2/(x^2*ln(4*x+2)^2+(2*x^3-20*x^2+50*x)*ln(4*x+2)+x^4-20*x^3+15
0*x^2-500*x+625))/(((2*x^4+x^3)*ln(4*x+2)^3+(6*x^5-57*x^4+120*x^3+75*x^2)*ln(4*x+2)^2+(6*x^6-117*x^5+840*x^4-2
550*x^3+2250*x^2+1875*x)*ln(4*x+2)+2*x^7-59*x^6+720*x^5-4625*x^4+16250*x^3-28125*x^2+12500*x+15625)*exp(81*x^2
/(x^2*ln(4*x+2)^2+(2*x^3-20*x^2+50*x)*ln(4*x+2)+x^4-20*x^3+150*x^2-500*x+625))+(6*x^4+3*x^3)*ln(4*x+2)^3+(18*x
^5-171*x^4+360*x^3+225*x^2)*ln(4*x+2)^2+(18*x^6-351*x^5+2520*x^4-7650*x^3+6750*x^2+5625*x)*ln(4*x+2)+6*x^7-177
*x^6+2160*x^5-13875*x^4+48750*x^3-84375*x^2+37500*x+46875),x,method=_RETURNVERBOSE)
[Out]
81*x^2/(ln(4*x+2)*x+x^2-10*x+25)^2-81*x^2/(x^2*ln(4*x+2)^2+(2*x^3-20*x^2+50*x)*ln(4*x+2)+x^4-20*x^3+150*x^2-50
0*x+625)+ln(exp(81*x^2/(ln(4*x+2)*x+x^2-10*x+25)^2)+3)
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maxima [B] time = 0.98, size = 555, normalized size = 19.82 \begin {gather*} -\frac {81 \, x \log \left (2 \, x + 1\right )}{x^{4} + 2 \, x^{3} {\left (\log \relax (2) - 10\right )} + x^{2} \log \left (2 \, x + 1\right )^{2} + {\left (\log \relax (2)^{2} - 20 \, \log \relax (2) + 150\right )} x^{2} + 50 \, x {\left (\log \relax (2) - 10\right )} + 2 \, {\left (x^{3} + x^{2} {\left (\log \relax (2) - 10\right )} + 25 \, x\right )} \log \left (2 \, x + 1\right ) + 625} + \log \left (\frac {1}{3} \, {\left (3 \, e^{\left (\frac {81 \, x \log \relax (2)}{x^{4} + 2 \, x^{3} {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + {\left (\log \relax (2)^{2} + 2 \, {\left (\log \relax (2) - 10\right )} \log \left (2 \, x + 1\right ) + \log \left (2 \, x + 1\right )^{2} - 20 \, \log \relax (2) + 150\right )} x^{2} + 50 \, x {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + 625} + \frac {81 \, x \log \left (2 \, x + 1\right )}{x^{4} + 2 \, x^{3} {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + {\left (\log \relax (2)^{2} + 2 \, {\left (\log \relax (2) - 10\right )} \log \left (2 \, x + 1\right ) + \log \left (2 \, x + 1\right )^{2} - 20 \, \log \relax (2) + 150\right )} x^{2} + 50 \, x {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + 625} + \frac {2025}{x^{4} + 2 \, x^{3} {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + {\left (\log \relax (2)^{2} + 2 \, {\left (\log \relax (2) - 10\right )} \log \left (2 \, x + 1\right ) + \log \left (2 \, x + 1\right )^{2} - 20 \, \log \relax (2) + 150\right )} x^{2} + 50 \, x {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + 625}\right )} + e^{\left (\frac {810 \, x}{x^{4} + 2 \, x^{3} {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + {\left (\log \relax (2)^{2} + 2 \, {\left (\log \relax (2) - 10\right )} \log \left (2 \, x + 1\right ) + \log \left (2 \, x + 1\right )^{2} - 20 \, \log \relax (2) + 150\right )} x^{2} + 50 \, x {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + 625} + \frac {81}{x^{2} + x {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + 25}\right )}\right )} e^{\left (-\frac {81 \, x \log \relax (2)}{x^{4} + 2 \, x^{3} {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + {\left (\log \relax (2)^{2} + 2 \, {\left (\log \relax (2) - 10\right )} \log \left (2 \, x + 1\right ) + \log \left (2 \, x + 1\right )^{2} - 20 \, \log \relax (2) + 150\right )} x^{2} + 50 \, x {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + 625} - \frac {2025}{x^{4} + 2 \, x^{3} {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + {\left (\log \relax (2)^{2} + 2 \, {\left (\log \relax (2) - 10\right )} \log \left (2 \, x + 1\right ) + \log \left (2 \, x + 1\right )^{2} - 20 \, \log \relax (2) + 150\right )} x^{2} + 50 \, x {\left (\log \relax (2) + \log \left (2 \, x + 1\right ) - 10\right )} + 625}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-324*x^4-486*x^3+8100*x^2+4050*x)*exp(81*x^2/(x^2*log(4*x+2)^2+(2*x^3-20*x^2+50*x)*log(4*x+2)+x^4-2
0*x^3+150*x^2-500*x+625))/(((2*x^4+x^3)*log(4*x+2)^3+(6*x^5-57*x^4+120*x^3+75*x^2)*log(4*x+2)^2+(6*x^6-117*x^5
+840*x^4-2550*x^3+2250*x^2+1875*x)*log(4*x+2)+2*x^7-59*x^6+720*x^5-4625*x^4+16250*x^3-28125*x^2+12500*x+15625)
*exp(81*x^2/(x^2*log(4*x+2)^2+(2*x^3-20*x^2+50*x)*log(4*x+2)+x^4-20*x^3+150*x^2-500*x+625))+(6*x^4+3*x^3)*log(
4*x+2)^3+(18*x^5-171*x^4+360*x^3+225*x^2)*log(4*x+2)^2+(18*x^6-351*x^5+2520*x^4-7650*x^3+6750*x^2+5625*x)*log(
4*x+2)+6*x^7-177*x^6+2160*x^5-13875*x^4+48750*x^3-84375*x^2+37500*x+46875),x, algorithm="maxima")
[Out]
-81*x*log(2*x + 1)/(x^4 + 2*x^3*(log(2) - 10) + x^2*log(2*x + 1)^2 + (log(2)^2 - 20*log(2) + 150)*x^2 + 50*x*(
log(2) - 10) + 2*(x^3 + x^2*(log(2) - 10) + 25*x)*log(2*x + 1) + 625) + log(1/3*(3*e^(81*x*log(2)/(x^4 + 2*x^3
*(log(2) + log(2*x + 1) - 10) + (log(2)^2 + 2*(log(2) - 10)*log(2*x + 1) + log(2*x + 1)^2 - 20*log(2) + 150)*x
^2 + 50*x*(log(2) + log(2*x + 1) - 10) + 625) + 81*x*log(2*x + 1)/(x^4 + 2*x^3*(log(2) + log(2*x + 1) - 10) +
(log(2)^2 + 2*(log(2) - 10)*log(2*x + 1) + log(2*x + 1)^2 - 20*log(2) + 150)*x^2 + 50*x*(log(2) + log(2*x + 1)
- 10) + 625) + 2025/(x^4 + 2*x^3*(log(2) + log(2*x + 1) - 10) + (log(2)^2 + 2*(log(2) - 10)*log(2*x + 1) + lo
g(2*x + 1)^2 - 20*log(2) + 150)*x^2 + 50*x*(log(2) + log(2*x + 1) - 10) + 625)) + e^(810*x/(x^4 + 2*x^3*(log(2
) + log(2*x + 1) - 10) + (log(2)^2 + 2*(log(2) - 10)*log(2*x + 1) + log(2*x + 1)^2 - 20*log(2) + 150)*x^2 + 50
*x*(log(2) + log(2*x + 1) - 10) + 625) + 81/(x^2 + x*(log(2) + log(2*x + 1) - 10) + 25)))*e^(-81*x*log(2)/(x^4
+ 2*x^3*(log(2) + log(2*x + 1) - 10) + (log(2)^2 + 2*(log(2) - 10)*log(2*x + 1) + log(2*x + 1)^2 - 20*log(2)
+ 150)*x^2 + 50*x*(log(2) + log(2*x + 1) - 10) + 625) - 2025/(x^4 + 2*x^3*(log(2) + log(2*x + 1) - 10) + (log(
2)^2 + 2*(log(2) - 10)*log(2*x + 1) + log(2*x + 1)^2 - 20*log(2) + 150)*x^2 + 50*x*(log(2) + log(2*x + 1) - 10
) + 625)))
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mupad [B] time = 7.00, size = 72, normalized size = 2.57 \begin {gather*} \ln \left ({\mathrm {e}}^{\frac {81\,x^2}{x^4+2\,x^3\,\ln \left (4\,x+2\right )-20\,x^3+x^2\,{\ln \left (4\,x+2\right )}^2-20\,x^2\,\ln \left (4\,x+2\right )+150\,x^2+50\,x\,\ln \left (4\,x+2\right )-500\,x+625}}+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((exp((81*x^2)/(x^2*log(4*x + 2)^2 - 500*x + log(4*x + 2)*(50*x - 20*x^2 + 2*x^3) + 150*x^2 - 20*x^3 + x^4
+ 625))*(4050*x + 8100*x^2 - 486*x^3 - 324*x^4))/(37500*x + log(4*x + 2)^3*(3*x^3 + 6*x^4) + log(4*x + 2)*(562
5*x + 6750*x^2 - 7650*x^3 + 2520*x^4 - 351*x^5 + 18*x^6) + log(4*x + 2)^2*(225*x^2 + 360*x^3 - 171*x^4 + 18*x^
5) - 84375*x^2 + 48750*x^3 - 13875*x^4 + 2160*x^5 - 177*x^6 + 6*x^7 + exp((81*x^2)/(x^2*log(4*x + 2)^2 - 500*x
+ log(4*x + 2)*(50*x - 20*x^2 + 2*x^3) + 150*x^2 - 20*x^3 + x^4 + 625))*(12500*x + log(4*x + 2)*(1875*x + 225
0*x^2 - 2550*x^3 + 840*x^4 - 117*x^5 + 6*x^6) + log(4*x + 2)^2*(75*x^2 + 120*x^3 - 57*x^4 + 6*x^5) + log(4*x +
2)^3*(x^3 + 2*x^4) - 28125*x^2 + 16250*x^3 - 4625*x^4 + 720*x^5 - 59*x^6 + 2*x^7 + 15625) + 46875),x)
[Out]
log(exp((81*x^2)/(x^2*log(4*x + 2)^2 - 500*x + 50*x*log(4*x + 2) + 150*x^2 - 20*x^3 + x^4 - 20*x^2*log(4*x + 2
) + 2*x^3*log(4*x + 2) + 625)) + 3)
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sympy [B] time = 5.02, size = 60, normalized size = 2.14 \begin {gather*} \log {\left (e^{\frac {81 x^{2}}{x^{4} - 20 x^{3} + x^{2} \log {\left (4 x + 2 \right )}^{2} + 150 x^{2} - 500 x + \left (2 x^{3} - 20 x^{2} + 50 x\right ) \log {\left (4 x + 2 \right )} + 625}} + 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-324*x**4-486*x**3+8100*x**2+4050*x)*exp(81*x**2/(x**2*ln(4*x+2)**2+(2*x**3-20*x**2+50*x)*ln(4*x+2)
+x**4-20*x**3+150*x**2-500*x+625))/(((2*x**4+x**3)*ln(4*x+2)**3+(6*x**5-57*x**4+120*x**3+75*x**2)*ln(4*x+2)**2
+(6*x**6-117*x**5+840*x**4-2550*x**3+2250*x**2+1875*x)*ln(4*x+2)+2*x**7-59*x**6+720*x**5-4625*x**4+16250*x**3-
28125*x**2+12500*x+15625)*exp(81*x**2/(x**2*ln(4*x+2)**2+(2*x**3-20*x**2+50*x)*ln(4*x+2)+x**4-20*x**3+150*x**2
-500*x+625))+(6*x**4+3*x**3)*ln(4*x+2)**3+(18*x**5-171*x**4+360*x**3+225*x**2)*ln(4*x+2)**2+(18*x**6-351*x**5+
2520*x**4-7650*x**3+6750*x**2+5625*x)*ln(4*x+2)+6*x**7-177*x**6+2160*x**5-13875*x**4+48750*x**3-84375*x**2+375
00*x+46875),x)
[Out]
log(exp(81*x**2/(x**4 - 20*x**3 + x**2*log(4*x + 2)**2 + 150*x**2 - 500*x + (2*x**3 - 20*x**2 + 50*x)*log(4*x
+ 2) + 625)) + 3)
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