3.38.45 \(\int \frac {50000+247000 x+57500 x^2-162500 x^3+375000 x^4+(30000+148200 x+34500 x^2-97500 x^3+225000 x^4) \log (\frac {25 x+(-3+30 x-75 x^2) \log (e^3 (4+x^2))}{3-30 x+75 x^2})+(6000+29640 x+6900 x^2-19500 x^3+45000 x^4) \log ^2(\frac {25 x+(-3+30 x-75 x^2) \log (e^3 (4+x^2))}{3-30 x+75 x^2})+(400+1976 x+460 x^2-1300 x^3+3000 x^4) \log ^3(\frac {25 x+(-3+30 x-75 x^2) \log (e^3 (4+x^2))}{3-30 x+75 x^2})}{100 x-500 x^2+25 x^3-125 x^4+(-12+180 x-903 x^2+1545 x^3-225 x^4+375 x^5) \log (e^3 (4+x^2))} \, dx\)

Optimal. Leaf size=30 \[ \left (5+\log \left (\frac {x}{3 \left (-\frac {1}{5}+x\right )^2}-\log \left (e^3 \left (4+x^2\right )\right )\right )\right )^4 \]

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Rubi [F]  time = 25.94, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {50000+247000 x+57500 x^2-162500 x^3+375000 x^4+\left (30000+148200 x+34500 x^2-97500 x^3+225000 x^4\right ) \log \left (\frac {25 x+\left (-3+30 x-75 x^2\right ) \log \left (e^3 \left (4+x^2\right )\right )}{3-30 x+75 x^2}\right )+\left (6000+29640 x+6900 x^2-19500 x^3+45000 x^4\right ) \log ^2\left (\frac {25 x+\left (-3+30 x-75 x^2\right ) \log \left (e^3 \left (4+x^2\right )\right )}{3-30 x+75 x^2}\right )+\left (400+1976 x+460 x^2-1300 x^3+3000 x^4\right ) \log ^3\left (\frac {25 x+\left (-3+30 x-75 x^2\right ) \log \left (e^3 \left (4+x^2\right )\right )}{3-30 x+75 x^2}\right )}{100 x-500 x^2+25 x^3-125 x^4+\left (-12+180 x-903 x^2+1545 x^3-225 x^4+375 x^5\right ) \log \left (e^3 \left (4+x^2\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(50000 + 247000*x + 57500*x^2 - 162500*x^3 + 375000*x^4 + (30000 + 148200*x + 34500*x^2 - 97500*x^3 + 2250
00*x^4)*Log[(25*x + (-3 + 30*x - 75*x^2)*Log[E^3*(4 + x^2)])/(3 - 30*x + 75*x^2)] + (6000 + 29640*x + 6900*x^2
- 19500*x^3 + 45000*x^4)*Log[(25*x + (-3 + 30*x - 75*x^2)*Log[E^3*(4 + x^2)])/(3 - 30*x + 75*x^2)]^2 + (400 +
1976*x + 460*x^2 - 1300*x^3 + 3000*x^4)*Log[(25*x + (-3 + 30*x - 75*x^2)*Log[E^3*(4 + x^2)])/(3 - 30*x + 75*x
^2)]^3)/(100*x - 500*x^2 + 25*x^3 - 125*x^4 + (-12 + 180*x - 903*x^2 + 1545*x^3 - 225*x^4 + 375*x^5)*Log[E^3*(
4 + x^2)]),x]

[Out]

-17500*Defer[Int][(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])^(-1), x] + (148500 + 30000*I)*Defer[Int][
1/((2*I - x)*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])), x] + 75000*Defer[Int][x/(9 - 115*x + 225*x^2
+ 3*(1 - 5*x)^2*Log[4 + x^2]), x] - (148500 - 30000*I)*Defer[Int][1/((2*I + x)*(9 - 115*x + 225*x^2 + 3*(1 -
5*x)^2*Log[4 + x^2])), x] + 25000*Defer[Int][1/((-1 + 5*x)*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2]))
, x] - 10500*Defer[Int][Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2]/(9 - 115*x +
225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2]), x] + (89100 + 18000*I)*Defer[Int][Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1
- 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2]/((2*I - x)*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])), x] + 45000
*Defer[Int][(x*Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2])/(9 - 115*x + 225*x^2
+ 3*(1 - 5*x)^2*Log[4 + x^2]), x] - (89100 - 18000*I)*Defer[Int][Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2
*Log[4 + x^2])/(1 - 5*x)^2]/((2*I + x)*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])), x] + 15000*Defer[I
nt][Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2]/((-1 + 5*x)*(9 - 115*x + 225*x^2
+ 3*(1 - 5*x)^2*Log[4 + x^2])), x] - 2100*Defer[Int][Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2
])/(1 - 5*x)^2]^2/(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2]), x] + (17820 + 3600*I)*Defer[Int][Log[-1/
3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2]^2/((2*I - x)*(9 - 115*x + 225*x^2 + 3*(1 - 5
*x)^2*Log[4 + x^2])), x] + 9000*Defer[Int][(x*Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 -
5*x)^2]^2)/(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2]), x] - (17820 - 3600*I)*Defer[Int][Log[-1/3*(9 -
115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2]^2/((2*I + x)*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*
Log[4 + x^2])), x] + 3000*Defer[Int][Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2]^
2/((-1 + 5*x)*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])), x] - 140*Defer[Int][Log[-1/3*(9 - 115*x + 2
25*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2]^3/(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2]), x] + (
1188 + 240*I)*Defer[Int][Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2]^3/((2*I - x)
*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])), x] + 600*Defer[Int][(x*Log[-1/3*(9 - 115*x + 225*x^2 + 3
*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2]^3)/(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2]), x] - (1188 - 24
0*I)*Defer[Int][Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2]^3/((2*I + x)*(9 - 115
*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])), x] + 200*Defer[Int][Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2
*Log[4 + x^2])/(1 - 5*x)^2]^3/((-1 + 5*x)*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (-100-494 x-115 x^2+325 x^3-750 x^4\right ) \left (5+\log \left (-\frac {9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )}{3 (1-5 x)^2}\right )\right )^3}{\left (4-20 x+x^2-5 x^3\right ) \left (9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )\right )} \, dx\\ &=4 \int \frac {\left (-100-494 x-115 x^2+325 x^3-750 x^4\right ) \left (5+\log \left (-\frac {9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )}{3 (1-5 x)^2}\right )\right )^3}{\left (4-20 x+x^2-5 x^3\right ) \left (9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )\right )} \, dx\\ &=4 \int \left (\frac {125 \left (100+494 x+115 x^2-325 x^3+750 x^4\right )}{(-1+5 x) \left (4+x^2\right ) \left (9-115 x+225 x^2+3 \log \left (4+x^2\right )-30 x \log \left (4+x^2\right )+75 x^2 \log \left (4+x^2\right )\right )}+\frac {75 \left (100+494 x+115 x^2-325 x^3+750 x^4\right ) \log \left (-\frac {9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )}{3 (1-5 x)^2}\right )}{(-1+5 x) \left (4+x^2\right ) \left (9-115 x+225 x^2+3 \log \left (4+x^2\right )-30 x \log \left (4+x^2\right )+75 x^2 \log \left (4+x^2\right )\right )}+\frac {15 \left (100+494 x+115 x^2-325 x^3+750 x^4\right ) \log ^2\left (-\frac {9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )}{3 (1-5 x)^2}\right )}{(-1+5 x) \left (4+x^2\right ) \left (9-115 x+225 x^2+3 \log \left (4+x^2\right )-30 x \log \left (4+x^2\right )+75 x^2 \log \left (4+x^2\right )\right )}+\frac {\left (100+494 x+115 x^2-325 x^3+750 x^4\right ) \log ^3\left (-\frac {9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )}{3 (1-5 x)^2}\right )}{(-1+5 x) \left (4+x^2\right ) \left (9-115 x+225 x^2+3 \log \left (4+x^2\right )-30 x \log \left (4+x^2\right )+75 x^2 \log \left (4+x^2\right )\right )}\right ) \, dx\\ &=4 \int \frac {\left (100+494 x+115 x^2-325 x^3+750 x^4\right ) \log ^3\left (-\frac {9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )}{3 (1-5 x)^2}\right )}{(-1+5 x) \left (4+x^2\right ) \left (9-115 x+225 x^2+3 \log \left (4+x^2\right )-30 x \log \left (4+x^2\right )+75 x^2 \log \left (4+x^2\right )\right )} \, dx+60 \int \frac {\left (100+494 x+115 x^2-325 x^3+750 x^4\right ) \log ^2\left (-\frac {9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )}{3 (1-5 x)^2}\right )}{(-1+5 x) \left (4+x^2\right ) \left (9-115 x+225 x^2+3 \log \left (4+x^2\right )-30 x \log \left (4+x^2\right )+75 x^2 \log \left (4+x^2\right )\right )} \, dx+300 \int \frac {\left (100+494 x+115 x^2-325 x^3+750 x^4\right ) \log \left (-\frac {9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )}{3 (1-5 x)^2}\right )}{(-1+5 x) \left (4+x^2\right ) \left (9-115 x+225 x^2+3 \log \left (4+x^2\right )-30 x \log \left (4+x^2\right )+75 x^2 \log \left (4+x^2\right )\right )} \, dx+500 \int \frac {100+494 x+115 x^2-325 x^3+750 x^4}{(-1+5 x) \left (4+x^2\right ) \left (9-115 x+225 x^2+3 \log \left (4+x^2\right )-30 x \log \left (4+x^2\right )+75 x^2 \log \left (4+x^2\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.09, size = 169, normalized size = 5.63 \begin {gather*} 4 \left (125 \log \left (-\frac {9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )}{3 (1-5 x)^2}\right )+\frac {75}{2} \log ^2\left (-\frac {9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )}{3 (1-5 x)^2}\right )+5 \log ^3\left (-\frac {9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )}{3 (1-5 x)^2}\right )+\frac {1}{4} \log ^4\left (-\frac {9-115 x+225 x^2+3 (1-5 x)^2 \log \left (4+x^2\right )}{3 (1-5 x)^2}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(50000 + 247000*x + 57500*x^2 - 162500*x^3 + 375000*x^4 + (30000 + 148200*x + 34500*x^2 - 97500*x^3
+ 225000*x^4)*Log[(25*x + (-3 + 30*x - 75*x^2)*Log[E^3*(4 + x^2)])/(3 - 30*x + 75*x^2)] + (6000 + 29640*x + 69
00*x^2 - 19500*x^3 + 45000*x^4)*Log[(25*x + (-3 + 30*x - 75*x^2)*Log[E^3*(4 + x^2)])/(3 - 30*x + 75*x^2)]^2 +
(400 + 1976*x + 460*x^2 - 1300*x^3 + 3000*x^4)*Log[(25*x + (-3 + 30*x - 75*x^2)*Log[E^3*(4 + x^2)])/(3 - 30*x
+ 75*x^2)]^3)/(100*x - 500*x^2 + 25*x^3 - 125*x^4 + (-12 + 180*x - 903*x^2 + 1545*x^3 - 225*x^4 + 375*x^5)*Log
[E^3*(4 + x^2)]),x]

[Out]

4*(125*Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2] + (75*Log[-1/3*(9 - 115*x + 22
5*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2]^2)/2 + 5*Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4
+ x^2])/(1 - 5*x)^2]^3 + Log[-1/3*(9 - 115*x + 225*x^2 + 3*(1 - 5*x)^2*Log[4 + x^2])/(1 - 5*x)^2]^4/4)

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fricas [B]  time = 0.58, size = 173, normalized size = 5.77 \begin {gather*} \log \left (-\frac {3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )} \log \left ({\left (x^{2} + 4\right )} e^{3}\right ) - 25 \, x}{3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )}}\right )^{4} + 20 \, \log \left (-\frac {3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )} \log \left ({\left (x^{2} + 4\right )} e^{3}\right ) - 25 \, x}{3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )}}\right )^{3} + 150 \, \log \left (-\frac {3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )} \log \left ({\left (x^{2} + 4\right )} e^{3}\right ) - 25 \, x}{3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )}}\right )^{2} + 500 \, \log \left (-\frac {3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )} \log \left ({\left (x^{2} + 4\right )} e^{3}\right ) - 25 \, x}{3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3000*x^4-1300*x^3+460*x^2+1976*x+400)*log(((-75*x^2+30*x-3)*log((x^2+4)*exp(3))+25*x)/(75*x^2-30*x
+3))^3+(45000*x^4-19500*x^3+6900*x^2+29640*x+6000)*log(((-75*x^2+30*x-3)*log((x^2+4)*exp(3))+25*x)/(75*x^2-30*
x+3))^2+(225000*x^4-97500*x^3+34500*x^2+148200*x+30000)*log(((-75*x^2+30*x-3)*log((x^2+4)*exp(3))+25*x)/(75*x^
2-30*x+3))+375000*x^4-162500*x^3+57500*x^2+247000*x+50000)/((375*x^5-225*x^4+1545*x^3-903*x^2+180*x-12)*log((x
^2+4)*exp(3))-125*x^4+25*x^3-500*x^2+100*x),x, algorithm="fricas")

[Out]

log(-1/3*(3*(25*x^2 - 10*x + 1)*log((x^2 + 4)*e^3) - 25*x)/(25*x^2 - 10*x + 1))^4 + 20*log(-1/3*(3*(25*x^2 - 1
0*x + 1)*log((x^2 + 4)*e^3) - 25*x)/(25*x^2 - 10*x + 1))^3 + 150*log(-1/3*(3*(25*x^2 - 10*x + 1)*log((x^2 + 4)
*e^3) - 25*x)/(25*x^2 - 10*x + 1))^2 + 500*log(-1/3*(3*(25*x^2 - 10*x + 1)*log((x^2 + 4)*e^3) - 25*x)/(25*x^2
- 10*x + 1))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {4 \, {\left (93750 \, x^{4} + {\left (750 \, x^{4} - 325 \, x^{3} + 115 \, x^{2} + 494 \, x + 100\right )} \log \left (-\frac {3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )} \log \left ({\left (x^{2} + 4\right )} e^{3}\right ) - 25 \, x}{3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )}}\right )^{3} - 40625 \, x^{3} + 15 \, {\left (750 \, x^{4} - 325 \, x^{3} + 115 \, x^{2} + 494 \, x + 100\right )} \log \left (-\frac {3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )} \log \left ({\left (x^{2} + 4\right )} e^{3}\right ) - 25 \, x}{3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )}}\right )^{2} + 14375 \, x^{2} + 75 \, {\left (750 \, x^{4} - 325 \, x^{3} + 115 \, x^{2} + 494 \, x + 100\right )} \log \left (-\frac {3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )} \log \left ({\left (x^{2} + 4\right )} e^{3}\right ) - 25 \, x}{3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )}}\right ) + 61750 \, x + 12500\right )}}{125 \, x^{4} - 25 \, x^{3} + 500 \, x^{2} - 3 \, {\left (125 \, x^{5} - 75 \, x^{4} + 515 \, x^{3} - 301 \, x^{2} + 60 \, x - 4\right )} \log \left ({\left (x^{2} + 4\right )} e^{3}\right ) - 100 \, x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3000*x^4-1300*x^3+460*x^2+1976*x+400)*log(((-75*x^2+30*x-3)*log((x^2+4)*exp(3))+25*x)/(75*x^2-30*x
+3))^3+(45000*x^4-19500*x^3+6900*x^2+29640*x+6000)*log(((-75*x^2+30*x-3)*log((x^2+4)*exp(3))+25*x)/(75*x^2-30*
x+3))^2+(225000*x^4-97500*x^3+34500*x^2+148200*x+30000)*log(((-75*x^2+30*x-3)*log((x^2+4)*exp(3))+25*x)/(75*x^
2-30*x+3))+375000*x^4-162500*x^3+57500*x^2+247000*x+50000)/((375*x^5-225*x^4+1545*x^3-903*x^2+180*x-12)*log((x
^2+4)*exp(3))-125*x^4+25*x^3-500*x^2+100*x),x, algorithm="giac")

[Out]

integrate(-4*(93750*x^4 + (750*x^4 - 325*x^3 + 115*x^2 + 494*x + 100)*log(-1/3*(3*(25*x^2 - 10*x + 1)*log((x^2
+ 4)*e^3) - 25*x)/(25*x^2 - 10*x + 1))^3 - 40625*x^3 + 15*(750*x^4 - 325*x^3 + 115*x^2 + 494*x + 100)*log(-1/
3*(3*(25*x^2 - 10*x + 1)*log((x^2 + 4)*e^3) - 25*x)/(25*x^2 - 10*x + 1))^2 + 14375*x^2 + 75*(750*x^4 - 325*x^3
+ 115*x^2 + 494*x + 100)*log(-1/3*(3*(25*x^2 - 10*x + 1)*log((x^2 + 4)*e^3) - 25*x)/(25*x^2 - 10*x + 1)) + 61
750*x + 12500)/(125*x^4 - 25*x^3 + 500*x^2 - 3*(125*x^5 - 75*x^4 + 515*x^3 - 301*x^2 + 60*x - 4)*log((x^2 + 4)
*e^3) - 100*x), x)

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maple [F]  time = 0.07, size = 0, normalized size = 0.00 \[\int \frac {\left (3000 x^{4}-1300 x^{3}+460 x^{2}+1976 x +400\right ) \ln \left (\frac {\left (-75 x^{2}+30 x -3\right ) \ln \left (\left (x^{2}+4\right ) {\mathrm e}^{3}\right )+25 x}{75 x^{2}-30 x +3}\right )^{3}+\left (45000 x^{4}-19500 x^{3}+6900 x^{2}+29640 x +6000\right ) \ln \left (\frac {\left (-75 x^{2}+30 x -3\right ) \ln \left (\left (x^{2}+4\right ) {\mathrm e}^{3}\right )+25 x}{75 x^{2}-30 x +3}\right )^{2}+\left (225000 x^{4}-97500 x^{3}+34500 x^{2}+148200 x +30000\right ) \ln \left (\frac {\left (-75 x^{2}+30 x -3\right ) \ln \left (\left (x^{2}+4\right ) {\mathrm e}^{3}\right )+25 x}{75 x^{2}-30 x +3}\right )+375000 x^{4}-162500 x^{3}+57500 x^{2}+247000 x +50000}{\left (375 x^{5}-225 x^{4}+1545 x^{3}-903 x^{2}+180 x -12\right ) \ln \left (\left (x^{2}+4\right ) {\mathrm e}^{3}\right )-125 x^{4}+25 x^{3}-500 x^{2}+100 x}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3000*x^4-1300*x^3+460*x^2+1976*x+400)*ln(((-75*x^2+30*x-3)*ln((x^2+4)*exp(3))+25*x)/(75*x^2-30*x+3))^3+(
45000*x^4-19500*x^3+6900*x^2+29640*x+6000)*ln(((-75*x^2+30*x-3)*ln((x^2+4)*exp(3))+25*x)/(75*x^2-30*x+3))^2+(2
25000*x^4-97500*x^3+34500*x^2+148200*x+30000)*ln(((-75*x^2+30*x-3)*ln((x^2+4)*exp(3))+25*x)/(75*x^2-30*x+3))+3
75000*x^4-162500*x^3+57500*x^2+247000*x+50000)/((375*x^5-225*x^4+1545*x^3-903*x^2+180*x-12)*ln((x^2+4)*exp(3))
-125*x^4+25*x^3-500*x^2+100*x),x)

[Out]

int(((3000*x^4-1300*x^3+460*x^2+1976*x+400)*ln(((-75*x^2+30*x-3)*ln((x^2+4)*exp(3))+25*x)/(75*x^2-30*x+3))^3+(
45000*x^4-19500*x^3+6900*x^2+29640*x+6000)*ln(((-75*x^2+30*x-3)*ln((x^2+4)*exp(3))+25*x)/(75*x^2-30*x+3))^2+(2
25000*x^4-97500*x^3+34500*x^2+148200*x+30000)*ln(((-75*x^2+30*x-3)*ln((x^2+4)*exp(3))+25*x)/(75*x^2-30*x+3))+3
75000*x^4-162500*x^3+57500*x^2+247000*x+50000)/((375*x^5-225*x^4+1545*x^3-903*x^2+180*x-12)*ln((x^2+4)*exp(3))
-125*x^4+25*x^3-500*x^2+100*x),x)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -4 \, \int \frac {93750 \, x^{4} + {\left (750 \, x^{4} - 325 \, x^{3} + 115 \, x^{2} + 494 \, x + 100\right )} \log \left (-\frac {3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )} \log \left ({\left (x^{2} + 4\right )} e^{3}\right ) - 25 \, x}{3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )}}\right )^{3} - 40625 \, x^{3} + 15 \, {\left (750 \, x^{4} - 325 \, x^{3} + 115 \, x^{2} + 494 \, x + 100\right )} \log \left (-\frac {3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )} \log \left ({\left (x^{2} + 4\right )} e^{3}\right ) - 25 \, x}{3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )}}\right )^{2} + 14375 \, x^{2} + 75 \, {\left (750 \, x^{4} - 325 \, x^{3} + 115 \, x^{2} + 494 \, x + 100\right )} \log \left (-\frac {3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )} \log \left ({\left (x^{2} + 4\right )} e^{3}\right ) - 25 \, x}{3 \, {\left (25 \, x^{2} - 10 \, x + 1\right )}}\right ) + 61750 \, x + 12500}{125 \, x^{4} - 25 \, x^{3} + 500 \, x^{2} - 3 \, {\left (125 \, x^{5} - 75 \, x^{4} + 515 \, x^{3} - 301 \, x^{2} + 60 \, x - 4\right )} \log \left ({\left (x^{2} + 4\right )} e^{3}\right ) - 100 \, x}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3000*x^4-1300*x^3+460*x^2+1976*x+400)*log(((-75*x^2+30*x-3)*log((x^2+4)*exp(3))+25*x)/(75*x^2-30*x
+3))^3+(45000*x^4-19500*x^3+6900*x^2+29640*x+6000)*log(((-75*x^2+30*x-3)*log((x^2+4)*exp(3))+25*x)/(75*x^2-30*
x+3))^2+(225000*x^4-97500*x^3+34500*x^2+148200*x+30000)*log(((-75*x^2+30*x-3)*log((x^2+4)*exp(3))+25*x)/(75*x^
2-30*x+3))+375000*x^4-162500*x^3+57500*x^2+247000*x+50000)/((375*x^5-225*x^4+1545*x^3-903*x^2+180*x-12)*log((x
^2+4)*exp(3))-125*x^4+25*x^3-500*x^2+100*x),x, algorithm="maxima")

[Out]

-4*integrate((93750*x^4 + (750*x^4 - 325*x^3 + 115*x^2 + 494*x + 100)*log(-1/3*(3*(25*x^2 - 10*x + 1)*log((x^2
+ 4)*e^3) - 25*x)/(25*x^2 - 10*x + 1))^3 - 40625*x^3 + 15*(750*x^4 - 325*x^3 + 115*x^2 + 494*x + 100)*log(-1/
3*(3*(25*x^2 - 10*x + 1)*log((x^2 + 4)*e^3) - 25*x)/(25*x^2 - 10*x + 1))^2 + 14375*x^2 + 75*(750*x^4 - 325*x^3
+ 115*x^2 + 494*x + 100)*log(-1/3*(3*(25*x^2 - 10*x + 1)*log((x^2 + 4)*e^3) - 25*x)/(25*x^2 - 10*x + 1)) + 61
750*x + 12500)/(125*x^4 - 25*x^3 + 500*x^2 - 3*(125*x^5 - 75*x^4 + 515*x^3 - 301*x^2 + 60*x - 4)*log((x^2 + 4)
*e^3) - 100*x), x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {247000\,x+\ln \left (\frac {25\,x-\ln \left ({\mathrm {e}}^3\,\left (x^2+4\right )\right )\,\left (75\,x^2-30\,x+3\right )}{75\,x^2-30\,x+3}\right )\,\left (225000\,x^4-97500\,x^3+34500\,x^2+148200\,x+30000\right )+{\ln \left (\frac {25\,x-\ln \left ({\mathrm {e}}^3\,\left (x^2+4\right )\right )\,\left (75\,x^2-30\,x+3\right )}{75\,x^2-30\,x+3}\right )}^3\,\left (3000\,x^4-1300\,x^3+460\,x^2+1976\,x+400\right )+{\ln \left (\frac {25\,x-\ln \left ({\mathrm {e}}^3\,\left (x^2+4\right )\right )\,\left (75\,x^2-30\,x+3\right )}{75\,x^2-30\,x+3}\right )}^2\,\left (45000\,x^4-19500\,x^3+6900\,x^2+29640\,x+6000\right )+57500\,x^2-162500\,x^3+375000\,x^4+50000}{100\,x-500\,x^2+25\,x^3-125\,x^4+\ln \left ({\mathrm {e}}^3\,\left (x^2+4\right )\right )\,\left (375\,x^5-225\,x^4+1545\,x^3-903\,x^2+180\,x-12\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((247000*x + log((25*x - log(exp(3)*(x^2 + 4))*(75*x^2 - 30*x + 3))/(75*x^2 - 30*x + 3))*(148200*x + 34500*
x^2 - 97500*x^3 + 225000*x^4 + 30000) + log((25*x - log(exp(3)*(x^2 + 4))*(75*x^2 - 30*x + 3))/(75*x^2 - 30*x
+ 3))^3*(1976*x + 460*x^2 - 1300*x^3 + 3000*x^4 + 400) + log((25*x - log(exp(3)*(x^2 + 4))*(75*x^2 - 30*x + 3)
)/(75*x^2 - 30*x + 3))^2*(29640*x + 6900*x^2 - 19500*x^3 + 45000*x^4 + 6000) + 57500*x^2 - 162500*x^3 + 375000
*x^4 + 50000)/(100*x - 500*x^2 + 25*x^3 - 125*x^4 + log(exp(3)*(x^2 + 4))*(180*x - 903*x^2 + 1545*x^3 - 225*x^
4 + 375*x^5 - 12)),x)

[Out]

int((247000*x + log((25*x - log(exp(3)*(x^2 + 4))*(75*x^2 - 30*x + 3))/(75*x^2 - 30*x + 3))*(148200*x + 34500*
x^2 - 97500*x^3 + 225000*x^4 + 30000) + log((25*x - log(exp(3)*(x^2 + 4))*(75*x^2 - 30*x + 3))/(75*x^2 - 30*x
+ 3))^3*(1976*x + 460*x^2 - 1300*x^3 + 3000*x^4 + 400) + log((25*x - log(exp(3)*(x^2 + 4))*(75*x^2 - 30*x + 3)
)/(75*x^2 - 30*x + 3))^2*(29640*x + 6900*x^2 - 19500*x^3 + 45000*x^4 + 6000) + 57500*x^2 - 162500*x^3 + 375000
*x^4 + 50000)/(100*x - 500*x^2 + 25*x^3 - 125*x^4 + log(exp(3)*(x^2 + 4))*(180*x - 903*x^2 + 1545*x^3 - 225*x^
4 + 375*x^5 - 12)), x)

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sympy [B]  time = 1.49, size = 141, normalized size = 4.70 \begin {gather*} \log {\left (\frac {25 x + \left (- 75 x^{2} + 30 x - 3\right ) \log {\left (\left (x^{2} + 4\right ) e^{3} \right )}}{75 x^{2} - 30 x + 3} \right )}^{4} + 20 \log {\left (\frac {25 x + \left (- 75 x^{2} + 30 x - 3\right ) \log {\left (\left (x^{2} + 4\right ) e^{3} \right )}}{75 x^{2} - 30 x + 3} \right )}^{3} + 150 \log {\left (\frac {25 x + \left (- 75 x^{2} + 30 x - 3\right ) \log {\left (\left (x^{2} + 4\right ) e^{3} \right )}}{75 x^{2} - 30 x + 3} \right )}^{2} + 500 \log {\left (- \frac {25 x}{75 x^{2} - 30 x + 3} + \log {\left (\left (x^{2} + 4\right ) e^{3} \right )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3000*x**4-1300*x**3+460*x**2+1976*x+400)*ln(((-75*x**2+30*x-3)*ln((x**2+4)*exp(3))+25*x)/(75*x**2-
30*x+3))**3+(45000*x**4-19500*x**3+6900*x**2+29640*x+6000)*ln(((-75*x**2+30*x-3)*ln((x**2+4)*exp(3))+25*x)/(75
*x**2-30*x+3))**2+(225000*x**4-97500*x**3+34500*x**2+148200*x+30000)*ln(((-75*x**2+30*x-3)*ln((x**2+4)*exp(3))
+25*x)/(75*x**2-30*x+3))+375000*x**4-162500*x**3+57500*x**2+247000*x+50000)/((375*x**5-225*x**4+1545*x**3-903*
x**2+180*x-12)*ln((x**2+4)*exp(3))-125*x**4+25*x**3-500*x**2+100*x),x)

[Out]

log((25*x + (-75*x**2 + 30*x - 3)*log((x**2 + 4)*exp(3)))/(75*x**2 - 30*x + 3))**4 + 20*log((25*x + (-75*x**2
+ 30*x - 3)*log((x**2 + 4)*exp(3)))/(75*x**2 - 30*x + 3))**3 + 150*log((25*x + (-75*x**2 + 30*x - 3)*log((x**2
+ 4)*exp(3)))/(75*x**2 - 30*x + 3))**2 + 500*log(-25*x/(75*x**2 - 30*x + 3) + log((x**2 + 4)*exp(3)))

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