3.69.0 ∫ x− 25________________________________ −84+8x+x2+e−4−2x+2x2x2+e−2−x+x2x(8+2x) (2100−200x−25x2+(200x+50x2) log(x)+e−4−2x+2x2 x2(−25+(50−50x+100x2) log(x))+e−2−x+x2 x(−200−50x+(200−100x+350x2+100x3) log(x))) 7056x−1344x2−104x3+16x4+x5+e−8−4x+4x2x5+e−6−3x+3x2x3(16x+4x2)+e−4−2x+2x2x2(−104x+48x2+6x3)+e−2−x+x2x(−1344x−208x2+48x3+4x4) dx [6885]

Integrand size = 262, antiderivative size = 27 \[ \int \frac {x^{-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (2100-200 x-25 x^2+\left (200 x+50 x^2\right ) \log (x)+e^{-4-2 x+2 x^2} x^2 \left (-25+\left (50-50 x+100 x^2\right ) \log (x)\right )+e^{-2-x+x^2} x \left (-200-50 x+\left (200-100 x+350 x^2+100 x^3\right ) \log (x)\right )\right )}{7056 x-1344 x^2-104 x^3+16 x^4+x^5+e^{-8-4 x+4 x^2} x^5+e^{-6-3 x+3 x^2} x^3 \left (16 x+4 x^2\right )+e^{-4-2 x+2 x^2} x^2 \left (-104 x+48 x^2+6 x^3\right )+e^{-2-x+x^2} x \left (-1344 x-208 x^2+48 x^3+4 x^4\right )} \, dx=x^{\frac {1}{4-\frac {1}{25} \left (4+x+e^{-2-x+x^2} x\right )^2}} \]

Rubi [F]

\[ \int \frac {x^{-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (2100-200 x-25 x^2+\left (200 x+50 x^2\right ) \log (x)+e^{-4-2 x+2 x^2} x^2 \left (-25+\left (50-50 x+100 x^2\right ) \log (x)\right )+e^{-2-x+x^2} x \left (-200-50 x+\left (200-100 x+350 x^2+100 x^3\right ) \log (x)\right )\right )}{7056 x-1344 x^2-104 x^3+16 x^4+x^5+e^{-8-4 x+4 x^2} x^5+e^{-6-3 x+3 x^2} x^3 \left (16 x+4 x^2\right )+e^{-4-2 x+2 x^2} x^2 \left (-104 x+48 x^2+6 x^3\right )+e^{-2-x+x^2} x \left (-1344 x-208 x^2+48 x^3+4 x^4\right )} \, dx=\int \frac {x^{-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (2100-200 x-25 x^2+\left (200 x+50 x^2\right ) \log (x)+e^{-4-2 x+2 x^2} x^2 \left (-25+\left (50-50 x+100 x^2\right ) \log (x)\right )+e^{-2-x+x^2} x \left (-200-50 x+\left (200-100 x+350 x^2+100 x^3\right ) \log (x)\right )\right )}{7056 x-1344 x^2-104 x^3+16 x^4+x^5+e^{-8-4 x+4 x^2} x^5+e^{-6-3 x+3 x^2} x^3 \left (16 x+4 x^2\right )+e^{-4-2 x+2 x^2} x^2 \left (-104 x+48 x^2+6 x^3\right )+e^{-2-x+x^2} x \left (-1344 x-208 x^2+48 x^3+4 x^4\right )} \, dx \]

Int[(2100 - 200*x - 25*x^2 + (200*x + 50*x^2)*Log[x] + E^(-4 - 2*x + 2*x^2)*x^2*(-25 + (50 - 50*x + 100*x^2)*L

og[x]) + E^(-2 - x + x^2)*x*(-200 - 50*x + (200 - 100*x + 350*x^2 + 100*x^3)*Log[x]))/(x^(25/(-84 + 8*x + x^2

+ E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x)))*(7056*x - 1344*x^2 - 104*x^3 + 16*x^4 + x^5 + E^(-

8 - 4*x + 4*x^2)*x^5 + E^(-6 - 3*x + 3*x^2)*x^3*(16*x + 4*x^2) + E^(-4 - 2*x + 2*x^2)*x^2*(-104*x + 48*x^2 + 6

(-15*Log[x]*Defer[Int][E^(4 + 2*x)/(x^(25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8

+ 2*x)))*(-6*E^(2 + x) + E^x^2*x + E^(2 + x)*x)^2), x])/2 + (15*Log[x]*Defer[Int][(E^(4 + 2*x)*x^(-1 - 25/(-84

+ 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(-6*E^(2 + x) + E^x^2*x + E^(2 + x)*

x)^2, x])/2 + (65*Log[x]*Defer[Int][(E^(4 + 2*x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2

- x + x^2)*x*(8 + 2*x))))/(-6*E^(2 + x) + E^x^2*x + E^(2 + x)*x)^2, x])/4 - (5*Log[x]*Defer[Int][(E^(4 + 2*x)

*x^(2 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(-6*E^(2 + x) + E^x^2

*x + E^(2 + x)*x)^2, x])/2 - (5*Log[x]*Defer[Int][E^(2 + x)/(x^(25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2

+ E^(-2 - x + x^2)*x*(8 + 2*x)))*(-6*E^(2 + x) + E^x^2*x + E^(2 + x)*x)), x])/4 - (5*Defer[Int][(E^(2 + x)*x^

(-1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(-6*E^(2 + x) + E^x^2*x

+ E^(2 + x)*x), x])/4 + (5*Log[x]*Defer[Int][(E^(2 + x)*x^(-1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^

2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(-6*E^(2 + x) + E^x^2*x + E^(2 + x)*x), x])/4 + (5*Log[x]*Defer[Int][(E^(2

+ x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(-6*E^(2 + x) +

E^x^2*x + E^(2 + x)*x), x])/2 - (35*Log[x]*Defer[Int][E^(4 + 2*x)/(x^(25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^

2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x)))*(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x)^2), x])/2 + (35*Log[x]*Defer[In

t][(E^(4 + 2*x)*x^(-1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(14*E

^(2 + x) + E^x^2*x + E^(2 + x)*x)^2, x])/2 + (135*Log[x]*Defer[Int][(E^(4 + 2*x)*x^(1 - 25/(-84 + 8*x + x^2 +

E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x)^2, x])/4 + (

5*Log[x]*Defer[Int][(E^(4 + 2*x)*x^(2 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8

+ 2*x))))/(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x)^2, x])/2 + (5*Log[x]*Defer[Int][E^(2 + x)/(x^(25/(-84 + 8*x

+ x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x)))*(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x)), x])

/4 + (5*Defer[Int][(E^(2 + x)*x^(-1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 +

2*x))))/(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x), x])/4 - (5*Log[x]*Defer[Int][(E^(2 + x)*x^(-1 - 25/(-84 + 8*x

+ x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x), x]

)/4 - (5*Log[x]*Defer[Int][(E^(2 + x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)

*x*(8 + 2*x))))/(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x), x])/2 + (15*Defer[Int][Defer[Int][E^(4 + 2*x)/(x^(25/(

-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x)))*(E^(2 + x)*(-6 + x) + E^x^2*x)^2),

x]/x, x])/2 - (15*Defer[Int][Defer[Int][(E^(4 + 2*x)*x^(-1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 +

2*E^(-2 - x + x^2)*x*(4 + x))))/(E^(2 + x)*(-6 + x) + E^x^2*x)^2, x]/x, x])/2 - (65*Defer[Int][Defer[Int][(E^

(4 + 2*x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x))))/(E^(2 + x)*(

-6 + x) + E^x^2*x)^2, x]/x, x])/4 + (5*Defer[Int][Defer[Int][(E^(4 + 2*x)*x^(2 - 25/(-84 + 8*x + x^2 + E^(-4 -

2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x))))/(E^(2 + x)*(-6 + x) + E^x^2*x)^2, x]/x, x])/2 + (5*Defer[I

nt][Defer[Int][E^(2 + x)/(x^(25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x)))*(

E^(2 + x)*(-6 + x) + E^x^2*x)), x]/x, x])/4 - (5*Defer[Int][Defer[Int][(E^(2 + x)*x^(-1 - 25/(-84 + 8*x + x^2

+ E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x))))/(E^(2 + x)*(-6 + x) + E^x^2*x), x]/x, x])/4 - (5*

Defer[Int][Defer[Int][(E^(2 + x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*

(4 + x))))/(E^(2 + x)*(-6 + x) + E^x^2*x), x]/x, x])/2 + (35*Defer[Int][Defer[Int][E^(4 + 2*x)/(x^(25/(-84 + 8

*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x)))*(E^x^2*x + E^(2 + x)*(14 + x))^2), x]/x,

x])/2 - (35*Defer[Int][Defer[Int][(E^(4 + 2*x)*x^(-1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-

2 - x + x^2)*x*(4 + x))))/(E^x^2*x + E^(2 + x)*(14 + x))^2, x]/x, x])/2 - (135*Defer[Int][Defer[Int][(E^(4 + 2

*x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x))))/(E^x^2*x + E^(2 +

x)*(14 + x))^2, x]/x, x])/4 - (5*Defer[Int][Defer[Int][(E^(4 + 2*x)*x^(2 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x +

2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x))))/(E^x^2*x + E^(2 + x)*(14 + x))^2, x]/x, x])/2 - (5*Defer[Int][De

fer[Int][E^(2 + x)/(x^(25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x)))*(E^x^2*

x + E^(2 + x)*(14 + x))), x]/x, x])/4 + (5*Defer[Int][Defer[Int][(E^(2 + x)*x^(-1 - 25/(-84 + 8*x + x^2 + E^(-

4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x))))/(E^x^2*x + E^(2 + x)*(14 + x)), x]/x, x])/4 + (5*Defer[

Int][Defer[Int][(E^(2 + x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x

Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{8+4 x} x^{-1-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (2100-200 x-25 x^2+\left (200 x+50 x^2\right ) \log (x)+e^{-4-2 x+2 x^2} x^2 \left (-25+\left (50-50 x+100 x^2\right ) \log (x)\right )+e^{-2-x+x^2} x \left (-200-50 x+\left (200-100 x+350 x^2+100 x^3\right ) \log (x)\right )\right )}{\left (84 e^{4+2 x}-8 e^{4+2 x} x-8 e^{2+x+x^2} x-e^{2 x^2} x^2-e^{4+2 x} x^2-2 e^{2+x+x^2} x^2\right )^2} \, dx \\ & = \int \left (-\frac {5 e^{4+2 x} x^{-1-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (-6+6 x-13 x^2+2 x^3\right ) \log (x)}{4 \left (-6 e^{2+x}+e^{x^2} x+e^{2+x} x\right )^2}+\frac {5 e^{4+2 x} x^{-1-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (14-14 x+27 x^2+2 x^3\right ) \log (x)}{4 \left (14 e^{2+x}+e^{x^2} x+e^{2+x} x\right )^2}+\frac {5 e^{2+x} x^{-1-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (-1+\log (x)-x \log (x)+2 x^2 \log (x)\right )}{4 \left (-6 e^{2+x}+e^{x^2} x+e^{2+x} x\right )}-\frac {5 e^{2+x} x^{-1-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (-1+\log (x)-x \log (x)+2 x^2 \log (x)\right )}{4 \left (14 e^{2+x}+e^{x^2} x+e^{2+x} x\right )}\right ) \, dx \\ & = -\left (\frac {5}{4} \int \frac {e^{4+2 x} x^{-1-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (-6+6 x-13 x^2+2 x^3\right ) \log (x)}{\left (-6 e^{2+x}+e^{x^2} x+e^{2+x} x\right )^2} \, dx\right )+\frac {5}{4} \int \frac {e^{4+2 x} x^{-1-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (14-14 x+27 x^2+2 x^3\right ) \log (x)}{\left (14 e^{2+x}+e^{x^2} x+e^{2+x} x\right )^2} \, dx+\frac {5}{4} \int \frac {e^{2+x} x^{-1-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (-1+\log (x)-x \log (x)+2 x^2 \log (x)\right )}{-6 e^{2+x}+e^{x^2} x+e^{2+x} x} \, dx-\frac {5}{4} \int \frac {e^{2+x} x^{-1-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (-1+\log (x)-x \log (x)+2 x^2 \log (x)\right )}{14 e^{2+x}+e^{x^2} x+e^{2+x} x} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [F]

Integrate[(2100 - 200*x - 25*x^2 + (200*x + 50*x^2)*Log[x] + E^(-4 - 2*x + 2*x^2)*x^2*(-25 + (50 - 50*x + 100*

x^2)*Log[x]) + E^(-2 - x + x^2)*x*(-200 - 50*x + (200 - 100*x + 350*x^2 + 100*x^3)*Log[x]))/(x^(25/(-84 + 8*x

+ x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x)))*(7056*x - 1344*x^2 - 104*x^3 + 16*x^4 + x^5

+ E^(-8 - 4*x + 4*x^2)*x^5 + E^(-6 - 3*x + 3*x^2)*x^3*(16*x + 4*x^2) + E^(-4 - 2*x + 2*x^2)*x^2*(-104*x + 48*x

Integrate[(2100 - 200*x - 25*x^2 + (200*x + 50*x^2)*Log[x] + E^(-4 - 2*x + 2*x^2)*x^2*(-25 + (50 - 50*x + 100*

x^2)*Log[x]) + E^(-2 - x + x^2)*x*(-200 - 50*x + (200 - 100*x + 350*x^2 + 100*x^3)*Log[x]))/(x^(25/(-84 + 8*x

+ x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x)))*(7056*x - 1344*x^2 - 104*x^3 + 16*x^4 + x^5

+ E^(-8 - 4*x + 4*x^2)*x^5 + E^(-6 - 3*x + 3*x^2)*x^3*(16*x + 4*x^2) + E^(-4 - 2*x + 2*x^2)*x^2*(-104*x + 48*x

Maple [A] (veriﬁed)

Time = 205.26 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.93


method	result	size

risch	\(x^{-\frac {25}{x^{2} {\mathrm e}^{2 \left (1+x \right ) \left (-2+x \right )}+2 \,{\mathrm e}^{\left (1+x \right ) \left (-2+x \right )} x^{2}+8 x \,{\mathrm e}^{\left (1+x \right ) \left (-2+x \right )}+x^{2}+8 x -84}}\)	\(52\)
parallelrisch	\({\mathrm e}^{-\frac {25 \ln \left (x \right )}{x^{2} {\mathrm e}^{2 x^{2}-2 x -4}+2 \,{\mathrm e}^{\ln \left (x \right )+x^{2}-x -2} x +x^{2}+8 \,{\mathrm e}^{\ln \left (x \right )+x^{2}-x -2}+8 x -84}}\)	\(56\)

int((((100*x^2-50*x+50)*ln(x)-25)*exp(ln(x)+x^2-x-2)^2+((100*x^3+350*x^2-100*x+200)*ln(x)-50*x-200)*exp(ln(x)+

x^2-x-2)+(50*x^2+200*x)*ln(x)-25*x^2-200*x+2100)*exp(-25*ln(x)/(exp(ln(x)+x^2-x-2)^2+(2*x+8)*exp(ln(x)+x^2-x-2

)+x^2+8*x-84))/(x*exp(ln(x)+x^2-x-2)^4+(4*x^2+16*x)*exp(ln(x)+x^2-x-2)^3+(6*x^3+48*x^2-104*x)*exp(ln(x)+x^2-x-

2)^2+(4*x^4+48*x^3-208*x^2-1344*x)*exp(ln(x)+x^2-x-2)+x^5+16*x^4-104*x^3-1344*x^2+7056*x),x,method=_RETURNVERB

Fricas [A] (veriﬁcation not implemented)

Time = 0.26 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.74 \[ \int \frac {x^{-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (2100-200 x-25 x^2+\left (200 x+50 x^2\right ) \log (x)+e^{-4-2 x+2 x^2} x^2 \left (-25+\left (50-50 x+100 x^2\right ) \log (x)\right )+e^{-2-x+x^2} x \left (-200-50 x+\left (200-100 x+350 x^2+100 x^3\right ) \log (x)\right )\right )}{7056 x-1344 x^2-104 x^3+16 x^4+x^5+e^{-8-4 x+4 x^2} x^5+e^{-6-3 x+3 x^2} x^3 \left (16 x+4 x^2\right )+e^{-4-2 x+2 x^2} x^2 \left (-104 x+48 x^2+6 x^3\right )+e^{-2-x+x^2} x \left (-1344 x-208 x^2+48 x^3+4 x^4\right )} \, dx=\frac {1}{x^{\frac {25}{x^{2} + 2 \, {\left (x + 4\right )} e^{\left (x^{2} - x + \log \left (x\right ) - 2\right )} + 8 \, x + e^{\left (2 \, x^{2} - 2 \, x + 2 \, \log \left (x\right ) - 4\right )} - 84}}} \]

integrate((((100*x^2-50*x+50)*log(x)-25)*exp(log(x)+x^2-x-2)^2+((100*x^3+350*x^2-100*x+200)*log(x)-50*x-200)*e

xp(log(x)+x^2-x-2)+(50*x^2+200*x)*log(x)-25*x^2-200*x+2100)*exp(-25*log(x)/(exp(log(x)+x^2-x-2)^2+(2*x+8)*exp(

log(x)+x^2-x-2)+x^2+8*x-84))/(x*exp(log(x)+x^2-x-2)^4+(4*x^2+16*x)*exp(log(x)+x^2-x-2)^3+(6*x^3+48*x^2-104*x)*

exp(log(x)+x^2-x-2)^2+(4*x^4+48*x^3-208*x^2-1344*x)*exp(log(x)+x^2-x-2)+x^5+16*x^4-104*x^3-1344*x^2+7056*x),x,

1/(x^(25/(x^2 + 2*(x + 4)*e^(x^2 - x + log(x) - 2) + 8*x + e^(2*x^2 - 2*x + 2*log(x) - 4) - 84)))

Sympy [A] (veriﬁcation not implemented)

Time = 3.14 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.70 \[ \int \frac {x^{-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (2100-200 x-25 x^2+\left (200 x+50 x^2\right ) \log (x)+e^{-4-2 x+2 x^2} x^2 \left (-25+\left (50-50 x+100 x^2\right ) \log (x)\right )+e^{-2-x+x^2} x \left (-200-50 x+\left (200-100 x+350 x^2+100 x^3\right ) \log (x)\right )\right )}{7056 x-1344 x^2-104 x^3+16 x^4+x^5+e^{-8-4 x+4 x^2} x^5+e^{-6-3 x+3 x^2} x^3 \left (16 x+4 x^2\right )+e^{-4-2 x+2 x^2} x^2 \left (-104 x+48 x^2+6 x^3\right )+e^{-2-x+x^2} x \left (-1344 x-208 x^2+48 x^3+4 x^4\right )} \, dx=e^{- \frac {25 \log {\left (x \right )}}{x^{2} e^{2 x^{2} - 2 x - 4} + x^{2} + x \left (2 x + 8\right ) e^{x^{2} - x - 2} + 8 x - 84}} \]

integrate((((100*x**2-50*x+50)*ln(x)-25)*exp(ln(x)+x**2-x-2)**2+((100*x**3+350*x**2-100*x+200)*ln(x)-50*x-200)

*exp(ln(x)+x**2-x-2)+(50*x**2+200*x)*ln(x)-25*x**2-200*x+2100)*exp(-25*ln(x)/(exp(ln(x)+x**2-x-2)**2+(2*x+8)*e

xp(ln(x)+x**2-x-2)+x**2+8*x-84))/(x*exp(ln(x)+x**2-x-2)**4+(4*x**2+16*x)*exp(ln(x)+x**2-x-2)**3+(6*x**3+48*x**

2-104*x)*exp(ln(x)+x**2-x-2)**2+(4*x**4+48*x**3-208*x**2-1344*x)*exp(ln(x)+x**2-x-2)+x**5+16*x**4-104*x**3-134

Maxima [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (26) = 52\).

Time = 0.60 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.22 \[ \int \frac {x^{-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (2100-200 x-25 x^2+\left (200 x+50 x^2\right ) \log (x)+e^{-4-2 x+2 x^2} x^2 \left (-25+\left (50-50 x+100 x^2\right ) \log (x)\right )+e^{-2-x+x^2} x \left (-200-50 x+\left (200-100 x+350 x^2+100 x^3\right ) \log (x)\right )\right )}{7056 x-1344 x^2-104 x^3+16 x^4+x^5+e^{-8-4 x+4 x^2} x^5+e^{-6-3 x+3 x^2} x^3 \left (16 x+4 x^2\right )+e^{-4-2 x+2 x^2} x^2 \left (-104 x+48 x^2+6 x^3\right )+e^{-2-x+x^2} x \left (-1344 x-208 x^2+48 x^3+4 x^4\right )} \, dx=e^{\left (\frac {5 \, e^{\left (x + 2\right )} \log \left (x\right )}{4 \, {\left (x e^{\left (x^{2}\right )} + {\left (x e^{2} + 14 \, e^{2}\right )} e^{x}\right )}} - \frac {5 \, e^{\left (x + 2\right )} \log \left (x\right )}{4 \, {\left (x e^{\left (x^{2}\right )} + {\left (x e^{2} - 6 \, e^{2}\right )} e^{x}\right )}}\right )} \]

integrate((((100*x^2-50*x+50)*log(x)-25)*exp(log(x)+x^2-x-2)^2+((100*x^3+350*x^2-100*x+200)*log(x)-50*x-200)*e

xp(log(x)+x^2-x-2)+(50*x^2+200*x)*log(x)-25*x^2-200*x+2100)*exp(-25*log(x)/(exp(log(x)+x^2-x-2)^2+(2*x+8)*exp(

log(x)+x^2-x-2)+x^2+8*x-84))/(x*exp(log(x)+x^2-x-2)^4+(4*x^2+16*x)*exp(log(x)+x^2-x-2)^3+(6*x^3+48*x^2-104*x)*

exp(log(x)+x^2-x-2)^2+(4*x^4+48*x^3-208*x^2-1344*x)*exp(log(x)+x^2-x-2)+x^5+16*x^4-104*x^3-1344*x^2+7056*x),x,

e^(5/4*e^(x + 2)*log(x)/(x*e^(x^2) + (x*e^2 + 14*e^2)*e^x) - 5/4*e^(x + 2)*log(x)/(x*e^(x^2) + (x*e^2 - 6*e^2)

Giac [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (26) = 52\).

Time = 8.91 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.11 \[ \int \frac {x^{-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (2100-200 x-25 x^2+\left (200 x+50 x^2\right ) \log (x)+e^{-4-2 x+2 x^2} x^2 \left (-25+\left (50-50 x+100 x^2\right ) \log (x)\right )+e^{-2-x+x^2} x \left (-200-50 x+\left (200-100 x+350 x^2+100 x^3\right ) \log (x)\right )\right )}{7056 x-1344 x^2-104 x^3+16 x^4+x^5+e^{-8-4 x+4 x^2} x^5+e^{-6-3 x+3 x^2} x^3 \left (16 x+4 x^2\right )+e^{-4-2 x+2 x^2} x^2 \left (-104 x+48 x^2+6 x^3\right )+e^{-2-x+x^2} x \left (-1344 x-208 x^2+48 x^3+4 x^4\right )} \, dx=\frac {1}{x^{\frac {25}{x^{2} e^{\left (2 \, x^{2} - 2 \, x - 4\right )} + 2 \, x^{2} e^{\left (x^{2} - x - 2\right )} + x^{2} + 8 \, x e^{\left (x^{2} - x - 2\right )} + 8 \, x - 84}}} \]

integrate((((100*x^2-50*x+50)*log(x)-25)*exp(log(x)+x^2-x-2)^2+((100*x^3+350*x^2-100*x+200)*log(x)-50*x-200)*e

xp(log(x)+x^2-x-2)+(50*x^2+200*x)*log(x)-25*x^2-200*x+2100)*exp(-25*log(x)/(exp(log(x)+x^2-x-2)^2+(2*x+8)*exp(

log(x)+x^2-x-2)+x^2+8*x-84))/(x*exp(log(x)+x^2-x-2)^4+(4*x^2+16*x)*exp(log(x)+x^2-x-2)^3+(6*x^3+48*x^2-104*x)*

exp(log(x)+x^2-x-2)^2+(4*x^4+48*x^3-208*x^2-1344*x)*exp(log(x)+x^2-x-2)+x^5+16*x^4-104*x^3-1344*x^2+7056*x),x,

1/(x^(25/(x^2*e^(2*x^2 - 2*x - 4) + 2*x^2*e^(x^2 - x - 2) + x^2 + 8*x*e^(x^2 - x - 2) + 8*x - 84)))

Mupad [B] (veriﬁcation not implemented)

Time = 12.34 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.22 \[ \int \frac {x^{-\frac {25}{-84+8 x+x^2+e^{-4-2 x+2 x^2} x^2+e^{-2-x+x^2} x (8+2 x)}} \left (2100-200 x-25 x^2+\left (200 x+50 x^2\right ) \log (x)+e^{-4-2 x+2 x^2} x^2 \left (-25+\left (50-50 x+100 x^2\right ) \log (x)\right )+e^{-2-x+x^2} x \left (-200-50 x+\left (200-100 x+350 x^2+100 x^3\right ) \log (x)\right )\right )}{7056 x-1344 x^2-104 x^3+16 x^4+x^5+e^{-8-4 x+4 x^2} x^5+e^{-6-3 x+3 x^2} x^3 \left (16 x+4 x^2\right )+e^{-4-2 x+2 x^2} x^2 \left (-104 x+48 x^2+6 x^3\right )+e^{-2-x+x^2} x \left (-1344 x-208 x^2+48 x^3+4 x^4\right )} \, dx=\frac {1}{x^{\frac {25}{8\,x+x^2+2\,x^2\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-2}+x^2\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^{2\,x^2}+8\,x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-2}-84}}} \]

int(-(exp(-(25*log(x))/(8*x + exp(2*log(x) - 2*x + 2*x^2 - 4) + x^2 + exp(log(x) - x + x^2 - 2)*(2*x + 8) - 84

))*(200*x - exp(2*log(x) - 2*x + 2*x^2 - 4)*(log(x)*(100*x^2 - 50*x + 50) - 25) - log(x)*(200*x + 50*x^2) + ex

p(log(x) - x + x^2 - 2)*(50*x - log(x)*(350*x^2 - 100*x + 100*x^3 + 200) + 200) + 25*x^2 - 2100))/(7056*x + ex

p(2*log(x) - 2*x + 2*x^2 - 4)*(48*x^2 - 104*x + 6*x^3) - exp(log(x) - x + x^2 - 2)*(1344*x + 208*x^2 - 48*x^3

- 4*x^4) - 1344*x^2 - 104*x^3 + 16*x^4 + x^5 + exp(3*log(x) - 3*x + 3*x^2 - 6)*(16*x + 4*x^2) + x*exp(4*log(x)

1/x^(25/(8*x + x^2 + 2*x^2*exp(-x)*exp(x^2)*exp(-2) + x^2*exp(-2*x)*exp(-4)*exp(2*x^2) + 8*x*exp(-x)*exp(x^2)*

Optimal result

Rubi [F]

Mathematica [F]

Maple [A] (veriﬁed)

Fricas [A] (veriﬁcation not implemented)

Sympy [A] (veriﬁcation not implemented)

Maxima [B] (veriﬁcation not implemented)

Giac [B] (veriﬁcation not implemented)

Mupad [B] (veriﬁcation not implemented)