3.90.47 \(\int \frac {e^6 x^2 (-40+100 x-102 x^2+48 x^3-10 x^4+(40-50 x+34 x^2-12 x^3+2 x^4) \log (20 x-25 x^2+17 x^3-6 x^4+x^5))}{(20 x-25 x^2+17 x^3-6 x^4+x^5) \log ^3(20 x-25 x^2+17 x^3-6 x^4+x^5)} \, dx\)

Optimal. Leaf size=26 \[ \frac {e^6 x^2}{\log ^2\left (x \left (4-x+\left ((-2+x)^2+x\right )^2\right )\right )} \]

________________________________________________________________________________________

Rubi [F]  time = 2.82, 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 {e^6 x^2 \left (-40+100 x-102 x^2+48 x^3-10 x^4+\left (40-50 x+34 x^2-12 x^3+2 x^4\right ) \log \left (20 x-25 x^2+17 x^3-6 x^4+x^5\right )\right )}{\left (20 x-25 x^2+17 x^3-6 x^4+x^5\right ) \log ^3\left (20 x-25 x^2+17 x^3-6 x^4+x^5\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^6*x^2*(-40 + 100*x - 102*x^2 + 48*x^3 - 10*x^4 + (40 - 50*x + 34*x^2 - 12*x^3 + 2*x^4)*Log[20*x - 25*x^
2 + 17*x^3 - 6*x^4 + x^5]))/((20*x - 25*x^2 + 17*x^3 - 6*x^4 + x^5)*Log[20*x - 25*x^2 + 17*x^3 - 6*x^4 + x^5]^
3),x]

[Out]

-12*E^6*Defer[Int][Log[x*(20 - 25*x + 17*x^2 - 6*x^3 + x^4)]^(-3), x] - 10*E^6*Defer[Int][x/Log[x*(20 - 25*x +
17*x^2 - 6*x^3 + x^4)]^3, x] + 240*E^6*Defer[Int][1/((20 - 25*x + 17*x^2 - 6*x^3 + x^4)*Log[x*(20 - 25*x + 17
*x^2 - 6*x^3 + x^4)]^3), x] - 140*E^6*Defer[Int][x/((20 - 25*x + 17*x^2 - 6*x^3 + x^4)*Log[x*(20 - 25*x + 17*x
^2 - 6*x^3 + x^4)]^3), x] + 54*E^6*Defer[Int][x^2/((20 - 25*x + 17*x^2 - 6*x^3 + x^4)*Log[x*(20 - 25*x + 17*x^
2 - 6*x^3 + x^4)]^3), x] - 4*E^6*Defer[Int][x^3/((20 - 25*x + 17*x^2 - 6*x^3 + x^4)*Log[x*(20 - 25*x + 17*x^2
- 6*x^3 + x^4)]^3), x] + 2*E^6*Defer[Int][x/Log[x*(20 - 25*x + 17*x^2 - 6*x^3 + x^4)]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^6 \int \frac {x^2 \left (-40+100 x-102 x^2+48 x^3-10 x^4+\left (40-50 x+34 x^2-12 x^3+2 x^4\right ) \log \left (20 x-25 x^2+17 x^3-6 x^4+x^5\right )\right )}{\left (20 x-25 x^2+17 x^3-6 x^4+x^5\right ) \log ^3\left (20 x-25 x^2+17 x^3-6 x^4+x^5\right )} \, dx\\ &=e^6 \int \frac {x \left (-40+100 x-102 x^2+48 x^3-10 x^4+\left (40-50 x+34 x^2-12 x^3+2 x^4\right ) \log \left (20 x-25 x^2+17 x^3-6 x^4+x^5\right )\right )}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (20 x-25 x^2+17 x^3-6 x^4+x^5\right )} \, dx\\ &=e^6 \int \frac {x \left (-40+100 x-102 x^2+48 x^3-10 x^4+\left (40-50 x+34 x^2-12 x^3+2 x^4\right ) \log \left (20 x-25 x^2+17 x^3-6 x^4+x^5\right )\right )}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx\\ &=e^6 \int \left (-\frac {40 x}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}+\frac {100 x^2}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}-\frac {102 x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}+\frac {48 x^4}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}-\frac {10 x^5}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}+\frac {2 x}{\log ^2\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}\right ) \, dx\\ &=\left (2 e^6\right ) \int \frac {x}{\log ^2\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (10 e^6\right ) \int \frac {x^5}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (40 e^6\right ) \int \frac {x}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (48 e^6\right ) \int \frac {x^4}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (100 e^6\right ) \int \frac {x^2}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (102 e^6\right ) \int \frac {x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx\\ &=\left (2 e^6\right ) \int \frac {x}{\log ^2\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (10 e^6\right ) \int \left (\frac {6}{\log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}+\frac {x}{\log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}+\frac {-120+130 x-77 x^2+19 x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}\right ) \, dx-\left (40 e^6\right ) \int \frac {x}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (48 e^6\right ) \int \left (\frac {1}{\log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}+\frac {-20+25 x-17 x^2+6 x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}\right ) \, dx+\left (100 e^6\right ) \int \frac {x^2}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (102 e^6\right ) \int \frac {x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx\\ &=\left (2 e^6\right ) \int \frac {x}{\log ^2\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (10 e^6\right ) \int \frac {x}{\log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (10 e^6\right ) \int \frac {-120+130 x-77 x^2+19 x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (40 e^6\right ) \int \frac {x}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (48 e^6\right ) \int \frac {1}{\log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (48 e^6\right ) \int \frac {-20+25 x-17 x^2+6 x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (60 e^6\right ) \int \frac {1}{\log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (100 e^6\right ) \int \frac {x^2}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (102 e^6\right ) \int \frac {x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx\\ &=\left (2 e^6\right ) \int \frac {x}{\log ^2\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (10 e^6\right ) \int \left (-\frac {120}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}+\frac {130 x}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}-\frac {77 x^2}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}+\frac {19 x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}\right ) \, dx-\left (10 e^6\right ) \int \frac {x}{\log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (40 e^6\right ) \int \frac {x}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (48 e^6\right ) \int \left (-\frac {20}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}+\frac {25 x}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}-\frac {17 x^2}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}+\frac {6 x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )}\right ) \, dx+\left (48 e^6\right ) \int \frac {1}{\log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (60 e^6\right ) \int \frac {1}{\log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (100 e^6\right ) \int \frac {x^2}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (102 e^6\right ) \int \frac {x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx\\ &=\left (2 e^6\right ) \int \frac {x}{\log ^2\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (10 e^6\right ) \int \frac {x}{\log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (40 e^6\right ) \int \frac {x}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (48 e^6\right ) \int \frac {1}{\log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (60 e^6\right ) \int \frac {1}{\log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (100 e^6\right ) \int \frac {x^2}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (102 e^6\right ) \int \frac {x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (190 e^6\right ) \int \frac {x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (288 e^6\right ) \int \frac {x^3}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (770 e^6\right ) \int \frac {x^2}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (816 e^6\right ) \int \frac {x^2}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (960 e^6\right ) \int \frac {1}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (1200 e^6\right ) \int \frac {1}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx+\left (1200 e^6\right ) \int \frac {x}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx-\left (1300 e^6\right ) \int \frac {x}{\left (20-25 x+17 x^2-6 x^3+x^4\right ) \log ^3\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.04, size = 30, normalized size = 1.15 \begin {gather*} \frac {e^6 x^2}{\log ^2\left (x \left (20-25 x+17 x^2-6 x^3+x^4\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^6*x^2*(-40 + 100*x - 102*x^2 + 48*x^3 - 10*x^4 + (40 - 50*x + 34*x^2 - 12*x^3 + 2*x^4)*Log[20*x -
25*x^2 + 17*x^3 - 6*x^4 + x^5]))/((20*x - 25*x^2 + 17*x^3 - 6*x^4 + x^5)*Log[20*x - 25*x^2 + 17*x^3 - 6*x^4 +
x^5]^3),x]

[Out]

(E^6*x^2)/Log[x*(20 - 25*x + 17*x^2 - 6*x^3 + x^4)]^2

________________________________________________________________________________________

fricas [A]  time = 0.46, size = 31, normalized size = 1.19 \begin {gather*} \frac {x^{2} e^{6}}{\log \left (x^{5} - 6 \, x^{4} + 17 \, x^{3} - 25 \, x^{2} + 20 \, x\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^4-12*x^3+34*x^2-50*x+40)*log(x^5-6*x^4+17*x^3-25*x^2+20*x)-10*x^4+48*x^3-102*x^2+100*x-40)*exp
(3+log(x))^2/(x^5-6*x^4+17*x^3-25*x^2+20*x)/log(x^5-6*x^4+17*x^3-25*x^2+20*x)^3,x, algorithm="fricas")

[Out]

x^2*e^6/log(x^5 - 6*x^4 + 17*x^3 - 25*x^2 + 20*x)^2

________________________________________________________________________________________

giac [B]  time = 0.35, size = 57, normalized size = 2.19 \begin {gather*} \frac {x^{2} e^{6}}{\log \left (x^{4} - 6 \, x^{3} + 17 \, x^{2} - 25 \, x + 20\right )^{2} + 2 \, \log \left (x^{4} - 6 \, x^{3} + 17 \, x^{2} - 25 \, x + 20\right ) \log \relax (x) + \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^4-12*x^3+34*x^2-50*x+40)*log(x^5-6*x^4+17*x^3-25*x^2+20*x)-10*x^4+48*x^3-102*x^2+100*x-40)*exp
(3+log(x))^2/(x^5-6*x^4+17*x^3-25*x^2+20*x)/log(x^5-6*x^4+17*x^3-25*x^2+20*x)^3,x, algorithm="giac")

[Out]

x^2*e^6/(log(x^4 - 6*x^3 + 17*x^2 - 25*x + 20)^2 + 2*log(x^4 - 6*x^3 + 17*x^2 - 25*x + 20)*log(x) + log(x)^2)

________________________________________________________________________________________

maple [C]  time = 0.14, size = 200, normalized size = 7.69

method	result	size
risch	\(-\frac {4 \,{\mathrm e}^{6} x^{2}}{\left (\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x^{4}-6 x^{3}+17 x^{2}-25 x +20\right )\right ) \mathrm {csgn}\left (i x \left (x^{4}-6 x^{3}+17 x^{2}-25 x +20\right )\right )-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x^{4}-6 x^{3}+17 x^{2}-25 x +20\right )\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (x^{4}-6 x^{3}+17 x^{2}-25 x +20\right )\right ) \mathrm {csgn}\left (i x \left (x^{4}-6 x^{3}+17 x^{2}-25 x +20\right )\right )^{2}+\pi \mathrm {csgn}\left (i x \left (x^{4}-6 x^{3}+17 x^{2}-25 x +20\right )\right )^{3}+2 i \ln \relax (x )+2 i \ln \left (x^{4}-6 x^{3}+17 x^{2}-25 x +20\right )\right )^{2}}\)	\(200\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^4-12*x^3+34*x^2-50*x+40)*ln(x^5-6*x^4+17*x^3-25*x^2+20*x)-10*x^4+48*x^3-102*x^2+100*x-40)*exp(3+ln(x
))^2/(x^5-6*x^4+17*x^3-25*x^2+20*x)/ln(x^5-6*x^4+17*x^3-25*x^2+20*x)^3,x,method=_RETURNVERBOSE)

[Out]

-4*exp(6)*x^2/(Pi*csgn(I*x)*csgn(I*(x^4-6*x^3+17*x^2-25*x+20))*csgn(I*x*(x^4-6*x^3+17*x^2-25*x+20))-Pi*csgn(I*
x)*csgn(I*x*(x^4-6*x^3+17*x^2-25*x+20))^2-Pi*csgn(I*(x^4-6*x^3+17*x^2-25*x+20))*csgn(I*x*(x^4-6*x^3+17*x^2-25*
x+20))^2+Pi*csgn(I*x*(x^4-6*x^3+17*x^2-25*x+20))^3+2*I*ln(x)+2*I*ln(x^4-6*x^3+17*x^2-25*x+20))^2

________________________________________________________________________________________

maxima [B]  time = 0.40, size = 57, normalized size = 2.19 \begin {gather*} \frac {x^{2} e^{6}}{\log \left (x^{4} - 6 \, x^{3} + 17 \, x^{2} - 25 \, x + 20\right )^{2} + 2 \, \log \left (x^{4} - 6 \, x^{3} + 17 \, x^{2} - 25 \, x + 20\right ) \log \relax (x) + \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^4-12*x^3+34*x^2-50*x+40)*log(x^5-6*x^4+17*x^3-25*x^2+20*x)-10*x^4+48*x^3-102*x^2+100*x-40)*exp
(3+log(x))^2/(x^5-6*x^4+17*x^3-25*x^2+20*x)/log(x^5-6*x^4+17*x^3-25*x^2+20*x)^3,x, algorithm="maxima")

[Out]

x^2*e^6/(log(x^4 - 6*x^3 + 17*x^2 - 25*x + 20)^2 + 2*log(x^4 - 6*x^3 + 17*x^2 - 25*x + 20)*log(x) + log(x)^2)

________________________________________________________________________________________

mupad [B]  time = 8.34, size = 443, normalized size = 17.04 \begin {gather*} \frac {x^2\,{\mathrm {e}}^6-\frac {x^2\,\ln \left (x^5-6\,x^4+17\,x^3-25\,x^2+20\,x\right )\,{\mathrm {e}}^6\,\left (x^4-6\,x^3+17\,x^2-25\,x+20\right )}{5\,x^4-24\,x^3+51\,x^2-50\,x+20}}{{\ln \left (x^5-6\,x^4+17\,x^3-25\,x^2+20\,x\right )}^2}-\frac {18\,x\,{\mathrm {e}}^6}{125}+\frac {2\,x^2\,{\mathrm {e}}^6}{25}+\frac {\frac {x^2\,{\mathrm {e}}^6\,\left (x^4-6\,x^3+17\,x^2-25\,x+20\right )}{5\,x^4-24\,x^3+51\,x^2-50\,x+20}-\frac {x^2\,\ln \left (x^5-6\,x^4+17\,x^3-25\,x^2+20\,x\right )\,{\mathrm {e}}^6\,\left (x^4-6\,x^3+17\,x^2-25\,x+20\right )\,\left (10\,x^8-102\,x^7+492\,x^6-1451\,x^5+2854\,x^4-3945\,x^3+3860\,x^2-2500\,x+800\right )}{{\left (5\,x^4-24\,x^3+51\,x^2-50\,x+20\right )}^3}}{\ln \left (x^5-6\,x^4+17\,x^3-25\,x^2+20\,x\right )}-\frac {-615\,{\mathrm {e}}^6\,x^{11}+8856\,{\mathrm {e}}^6\,x^{10}-\frac {276842\,{\mathrm {e}}^6\,x^9}{5}+\frac {1073739\,{\mathrm {e}}^6\,x^8}{5}-\frac {2975451\,{\mathrm {e}}^6\,x^7}{5}+\frac {6478543\,{\mathrm {e}}^6\,x^6}{5}-2302308\,{\mathrm {e}}^6\,x^5+3344556\,{\mathrm {e}}^6\,x^4-3744080\,{\mathrm {e}}^6\,x^3+2877120\,{\mathrm {e}}^6\,x^2-1200000\,{\mathrm {e}}^6\,x+140800\,{\mathrm {e}}^6}{15625\,x^{12}-225000\,x^{11}+1558125\,x^{10}-6786750\,x^9+20580375\,x^8-45571500\,x^7+75313875\,x^6-93378750\,x^5+86070000\,x^4-57475000\,x^3+26400000\,x^2-7500000\,x+1000000} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*log(x) + 6)*(100*x + log(20*x - 25*x^2 + 17*x^3 - 6*x^4 + x^5)*(34*x^2 - 50*x - 12*x^3 + 2*x^4 + 40
) - 102*x^2 + 48*x^3 - 10*x^4 - 40))/(log(20*x - 25*x^2 + 17*x^3 - 6*x^4 + x^5)^3*(20*x - 25*x^2 + 17*x^3 - 6*
x^4 + x^5)),x)

[Out]

(x^2*exp(6) - (x^2*log(20*x - 25*x^2 + 17*x^3 - 6*x^4 + x^5)*exp(6)*(17*x^2 - 25*x - 6*x^3 + x^4 + 20))/(51*x^
2 - 50*x - 24*x^3 + 5*x^4 + 20))/log(20*x - 25*x^2 + 17*x^3 - 6*x^4 + x^5)^2 - (18*x*exp(6))/125 + (2*x^2*exp(
6))/25 + ((x^2*exp(6)*(17*x^2 - 25*x - 6*x^3 + x^4 + 20))/(51*x^2 - 50*x - 24*x^3 + 5*x^4 + 20) - (x^2*log(20*
x - 25*x^2 + 17*x^3 - 6*x^4 + x^5)*exp(6)*(17*x^2 - 25*x - 6*x^3 + x^4 + 20)*(3860*x^2 - 2500*x - 3945*x^3 + 2
854*x^4 - 1451*x^5 + 492*x^6 - 102*x^7 + 10*x^8 + 800))/(51*x^2 - 50*x - 24*x^3 + 5*x^4 + 20)^3)/log(20*x - 25
*x^2 + 17*x^3 - 6*x^4 + x^5) - (140800*exp(6) - 1200000*x*exp(6) + 2877120*x^2*exp(6) - 3744080*x^3*exp(6) + 3
344556*x^4*exp(6) - 2302308*x^5*exp(6) + (6478543*x^6*exp(6))/5 - (2975451*x^7*exp(6))/5 + (1073739*x^8*exp(6)
)/5 - (276842*x^9*exp(6))/5 + 8856*x^10*exp(6) - 615*x^11*exp(6))/(26400000*x^2 - 7500000*x - 57475000*x^3 + 8
6070000*x^4 - 93378750*x^5 + 75313875*x^6 - 45571500*x^7 + 20580375*x^8 - 6786750*x^9 + 1558125*x^10 - 225000*
x^11 + 15625*x^12 + 1000000)

________________________________________________________________________________________

sympy [A]  time = 0.23, size = 31, normalized size = 1.19 \begin {gather*} \frac {x^{2} e^{6}}{\log {\left (x^{5} - 6 x^{4} + 17 x^{3} - 25 x^{2} + 20 x \right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**4-12*x**3+34*x**2-50*x+40)*ln(x**5-6*x**4+17*x**3-25*x**2+20*x)-10*x**4+48*x**3-102*x**2+100*
x-40)*exp(3+ln(x))**2/(x**5-6*x**4+17*x**3-25*x**2+20*x)/ln(x**5-6*x**4+17*x**3-25*x**2+20*x)**3,x)

[Out]

x**2*exp(6)/log(x**5 - 6*x**4 + 17*x**3 - 25*x**2 + 20*x)**2

________________________________________________________________________________________