[next] [prev] [prev-tail] [tail] [up]

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

Optimal. Leaf size=27 \[ x^{\frac {1}{4-\frac {1}{25} \left (4+x+e^{-2-x+x^2} x\right )^2}} \]

________________________________________________________________________________________

Rubi [F]  time = 66.06, 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 {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 \end {gather*}

Verification is not applicable to the result.

[In]

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
*x^3) + E^(-2 - x + x^2)*x*(-1344*x - 208*x^2 + 48*x^3 + 4*x^4))),x]

[Out]

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

Rubi steps

\begin {gather*} \begin {aligned} \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 {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [F]  time = 2.19, size = 0, normalized size = 0.00 \begin {gather*} \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 \end {gather*}

Verification is not applicable to the result.

[In]

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
^2 + 6*x^3) + E^(-2 - x + x^2)*x*(-1344*x - 208*x^2 + 48*x^3 + 4*x^4))),x]

[Out]

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
^2 + 6*x^3) + E^(-2 - x + x^2)*x*(-1344*x - 208*x^2 + 48*x^3 + 4*x^4))), x]

________________________________________________________________________________________

fricas [A]  time = 3.18, size = 47, normalized size = 1.74 \begin {gather*} \frac {1}{x^{\frac {25}{x^{2} + 2 \, {\left (x + 4\right )} e^{\left (x^{2} - x + \log \relax (x) - 2\right )} + 8 \, x + e^{\left (2 \, x^{2} - 2 \, x + 2 \, \log \relax (x) - 4\right )} - 84}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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,
 algorithm="fricas")

[Out]

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)))

________________________________________________________________________________________

giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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,
 algorithm="giac")

[Out]

Timed out

________________________________________________________________________________________

maple [A]  time = 0.06, size = 52, normalized size = 1.93

method result size
risch \(x^{-\frac {25}{x^{2} {\mathrm e}^{2 \left (x +1\right ) \left (x -2\right )}+2 x^{2} {\mathrm e}^{\left (x +1\right ) \left (x -2\right )}+8 x \,{\mathrm e}^{\left (x +1\right ) \left (x -2\right )}+x^{2}+8 x -84}}\) \(52\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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
OSE)

[Out]

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

________________________________________________________________________________________

maxima [B]  time = 0.81, size = 60, normalized size = 2.22 \begin {gather*} e^{\left (\frac {5 \, e^{\left (x + 2\right )} \log \relax (x)}{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 \relax (x)}{4 \, {\left (x e^{\left (x^{2}\right )} + {\left (x e^{2} - 6 \, e^{2}\right )} e^{x}\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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,
 algorithm="maxima")

[Out]

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)
*e^x))

________________________________________________________________________________________

mupad [B]  time = 4.81, size = 60, normalized size = 2.22 \begin {gather*} \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}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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)
 - 4*x + 4*x^2 - 8)),x)

[Out]

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)*
exp(-2) - 84))

________________________________________________________________________________________

sympy [A]  time = 7.57, size = 46, normalized size = 1.70 \begin {gather*} e^{- \frac {25 \log {\relax (x )}}{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}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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
4*x**2+7056*x),x)

[Out]

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

________________________________________________________________________________________

[next] [prev] [prev-tail] [front] [up]