3.70.39 \(\int \frac {64+(-240 x+48 x^2) \log ^2(10)+(300 x^2-120 x^3+12 x^4) \log ^4(10)+(-125 x^3+75 x^4-15 x^5+x^6) \log ^6(10)+e^{\frac {-336+(640 x-128 x^2) \log ^2(10)+(-300 x^2+120 x^3-12 x^4) \log ^4(10)}{16+(-40 x+8 x^2) \log ^2(10)+(25 x^2-10 x^3+x^4) \log ^4(10)}} ((-800 x+320 x^2) \log ^2(10)+(800 x^2-480 x^3+64 x^4) \log ^4(10))}{64 x+(-240 x^2+48 x^3) \log ^2(10)+(300 x^3-120 x^4+12 x^5) \log ^4(10)+(-125 x^4+75 x^5-15 x^6+x^7) \log ^6(10)} \, dx\)

Optimal. Leaf size=28 \[ e^{4-\left (4+\frac {4}{4+(-5+x) x \log ^2(10)}\right )^2}+\log (x) \]

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Rubi [F]  time = 68.03, 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 {64+\left (-240 x+48 x^2\right ) \log ^2(10)+\left (300 x^2-120 x^3+12 x^4\right ) \log ^4(10)+\left (-125 x^3+75 x^4-15 x^5+x^6\right ) \log ^6(10)+\exp \left (\frac {-336+\left (640 x-128 x^2\right ) \log ^2(10)+\left (-300 x^2+120 x^3-12 x^4\right ) \log ^4(10)}{16+\left (-40 x+8 x^2\right ) \log ^2(10)+\left (25 x^2-10 x^3+x^4\right ) \log ^4(10)}\right ) \left (\left (-800 x+320 x^2\right ) \log ^2(10)+\left (800 x^2-480 x^3+64 x^4\right ) \log ^4(10)\right )}{64 x+\left (-240 x^2+48 x^3\right ) \log ^2(10)+\left (300 x^3-120 x^4+12 x^5\right ) \log ^4(10)+\left (-125 x^4+75 x^5-15 x^6+x^7\right ) \log ^6(10)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(64 + (-240*x + 48*x^2)*Log[10]^2 + (300*x^2 - 120*x^3 + 12*x^4)*Log[10]^4 + (-125*x^3 + 75*x^4 - 15*x^5 +
x^6)*Log[10]^6 + E^((-336 + (640*x - 128*x^2)*Log[10]^2 + (-300*x^2 + 120*x^3 - 12*x^4)*Log[10]^4)/(16 + (-40
*x + 8*x^2)*Log[10]^2 + (25*x^2 - 10*x^3 + x^4)*Log[10]^4))*((-800*x + 320*x^2)*Log[10]^2 + (800*x^2 - 480*x^3
+ 64*x^4)*Log[10]^4))/(64*x + (-240*x^2 + 48*x^3)*Log[10]^2 + (300*x^3 - 120*x^4 + 12*x^5)*Log[10]^4 + (-125*
x^4 + 75*x^5 - 15*x^6 + x^7)*Log[10]^6),x]

[Out]

(-1440*ArcTanh[((5 - 2*x)*Log[10])/Sqrt[-16 + 25*Log[10]^2]]*Log[10])/(-16 + 25*Log[10]^2)^(5/2) - (120*ArcTan
h[((5 - 2*x)*Log[10])/Sqrt[-16 + 25*Log[10]^2]]*Log[10]*(4 - 25*Log[10]^2))/(-16 + 25*Log[10]^2)^(5/2) - (6*(5
- x)^2*Log[10]^2*(8 - 5*x*Log[10]^2))/((16 - 25*Log[10]^2)*(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2) - (16*(8 -
25*Log[10]^2 + 5*x*Log[10]^2))/((16 - 25*Log[10]^2)*(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2) + (360*(5 - 2*x)*Lo
g[10]^2)/((16 - 25*Log[10]^2)^2*(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)) + (25*ArcTanh[((5 - 2*x)*Log[10])/Sqrt[-1
6 + 25*Log[10]^2]]*Log[10]*(96 - 200*Log[10]^2 + 125*Log[10]^4))/(-16 + 25*Log[10]^2)^(5/2) - (5*ArcTanh[((5 -
2*x)*Log[10])/Sqrt[-16 + 25*Log[10]^2]]*Log[10]*(96 - 400*Log[10]^2 + 625*Log[10]^4))/(-16 + 25*Log[10]^2)^(5
/2) + ((5 - x)^3*Log[10]^4*(20 + x*(8 - 25*Log[10]^2)))/(2*(16 - 25*Log[10]^2)*(4 - 5*x*Log[10]^2 + x^2*Log[10
]^2)^2) - (6*(128 - 1100*Log[10]^2 + 1875*Log[10]^4 + 15*x*Log[10]^2*(8 - 25*Log[10]^2)))/((16 - 25*Log[10]^2)
^2*(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)) + (4*(128 - 750*Log[10]^2 + 625*Log[10]^4 + 5*x*Log[10]^2*(28 - 25*Log
[10]^2)))/((16 - 25*Log[10]^2)^2*(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)) + ((5 - x)*Log[10]^2*(x*(256 - 300*Log[1
0]^2 - 625*Log[10]^4) - 5*(96 + 100*Log[10]^2 - 625*Log[10]^4)))/(2*(16 - 25*Log[10]^2)^2*(4 - 5*x*Log[10]^2 +
x^2*Log[10]^2)) + Log[x] + (1280*Log[10]^5*Defer[Int][1/(E^((4*(84 - 160*x*Log[10]^2 - 30*x^3*Log[10]^4 + 3*x
^4*Log[10]^4 + x^2*Log[10]^2*(32 + 75*Log[10]^2)))/(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2)*(5*Log[10]^2 - 2*x*L
og[10]^2 + Log[10]*Sqrt[-16 + 25*Log[10]^2])^3), x])/(-16 + 25*Log[10]^2)^(3/2) - (256*Log[10]^4*(5*Log[10] +
Sqrt[-16 + 25*Log[10]^2])*Defer[Int][1/(E^((4*(84 - 160*x*Log[10]^2 - 30*x^3*Log[10]^4 + 3*x^4*Log[10]^4 + x^2
*Log[10]^2*(32 + 75*Log[10]^2)))/(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2)*(5*Log[10]^2 - 2*x*Log[10]^2 + Log[10]
*Sqrt[-16 + 25*Log[10]^2])^3), x])/(-16 + 25*Log[10]^2)^(3/2) + (1920*Log[10]^4*Defer[Int][1/(E^((4*(84 - 160*
x*Log[10]^2 - 30*x^3*Log[10]^4 + 3*x^4*Log[10]^4 + x^2*Log[10]^2*(32 + 75*Log[10]^2)))/(4 - 5*x*Log[10]^2 + x^
2*Log[10]^2)^2)*(5*Log[10]^2 - 2*x*Log[10]^2 + Log[10]*Sqrt[-16 + 25*Log[10]^2])^2), x])/(16 - 25*Log[10]^2)^2
+ (640*Log[10]^4*Defer[Int][1/(E^((4*(84 - 160*x*Log[10]^2 - 30*x^3*Log[10]^4 + 3*x^4*Log[10]^4 + x^2*Log[10]
^2*(32 + 75*Log[10]^2)))/(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2)*(5*Log[10]^2 - 2*x*Log[10]^2 + Log[10]*Sqrt[-1
6 + 25*Log[10]^2])^2), x])/(16 - 25*Log[10]^2) - (128*Log[10]^3*(5*Log[10] + Sqrt[-16 + 25*Log[10]^2])*Defer[I
nt][1/(E^((4*(84 - 160*x*Log[10]^2 - 30*x^3*Log[10]^4 + 3*x^4*Log[10]^4 + x^2*Log[10]^2*(32 + 75*Log[10]^2)))/
(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2)*(5*Log[10]^2 - 2*x*Log[10]^2 + Log[10]*Sqrt[-16 + 25*Log[10]^2])^2), x]
)/(16 - 25*Log[10]^2) - (128*Log[10]^3*(15*Log[10] + Sqrt[-16 + 25*Log[10]^2])*Defer[Int][1/(E^((4*(84 - 160*x
*Log[10]^2 - 30*x^3*Log[10]^4 + 3*x^4*Log[10]^4 + x^2*Log[10]^2*(32 + 75*Log[10]^2)))/(4 - 5*x*Log[10]^2 + x^2
*Log[10]^2)^2)*(5*Log[10]^2 - 2*x*Log[10]^2 + Log[10]*Sqrt[-16 + 25*Log[10]^2])^2), x])/(16 - 25*Log[10]^2)^2
+ (1280*Log[10]^5*Defer[Int][1/(E^((4*(84 - 160*x*Log[10]^2 - 30*x^3*Log[10]^4 + 3*x^4*Log[10]^4 + x^2*Log[10]
^2*(32 + 75*Log[10]^2)))/(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2)*(-5*Log[10]^2 + 2*x*Log[10]^2 + Log[10]*Sqrt[-
16 + 25*Log[10]^2])^3), x])/(-16 + 25*Log[10]^2)^(3/2) - (256*Log[10]^4*(5*Log[10] - Sqrt[-16 + 25*Log[10]^2])
*Defer[Int][1/(E^((4*(84 - 160*x*Log[10]^2 - 30*x^3*Log[10]^4 + 3*x^4*Log[10]^4 + x^2*Log[10]^2*(32 + 75*Log[1
0]^2)))/(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2)*(-5*Log[10]^2 + 2*x*Log[10]^2 + Log[10]*Sqrt[-16 + 25*Log[10]^2
])^3), x])/(-16 + 25*Log[10]^2)^(3/2) + (1920*Log[10]^4*Defer[Int][1/(E^((4*(84 - 160*x*Log[10]^2 - 30*x^3*Log
[10]^4 + 3*x^4*Log[10]^4 + x^2*Log[10]^2*(32 + 75*Log[10]^2)))/(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2)*(-5*Log[
10]^2 + 2*x*Log[10]^2 + Log[10]*Sqrt[-16 + 25*Log[10]^2])^2), x])/(16 - 25*Log[10]^2)^2 + (640*Log[10]^4*Defer
[Int][1/(E^((4*(84 - 160*x*Log[10]^2 - 30*x^3*Log[10]^4 + 3*x^4*Log[10]^4 + x^2*Log[10]^2*(32 + 75*Log[10]^2))
)/(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2)*(-5*Log[10]^2 + 2*x*Log[10]^2 + Log[10]*Sqrt[-16 + 25*Log[10]^2])^2),
x])/(16 - 25*Log[10]^2) - (128*Log[10]^3*(5*Log[10] - Sqrt[-16 + 25*Log[10]^2])*Defer[Int][1/(E^((4*(84 - 160
*x*Log[10]^2 - 30*x^3*Log[10]^4 + 3*x^4*Log[10]^4 + x^2*Log[10]^2*(32 + 75*Log[10]^2)))/(4 - 5*x*Log[10]^2 + x
^2*Log[10]^2)^2)*(-5*Log[10]^2 + 2*x*Log[10]^2 + Log[10]*Sqrt[-16 + 25*Log[10]^2])^2), x])/(16 - 25*Log[10]^2)
- (128*Log[10]^3*(15*Log[10] - Sqrt[-16 + 25*Log[10]^2])*Defer[Int][1/(E^((4*(84 - 160*x*Log[10]^2 - 30*x^3*L
og[10]^4 + 3*x^4*Log[10]^4 + x^2*Log[10]^2*(32 + 75*Log[10]^2)))/(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2)*(-5*Lo
g[10]^2 + 2*x*Log[10]^2 + Log[10]*Sqrt[-16 + 25*Log[10]^2])^2), x])/(16 - 25*Log[10]^2)^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {64+48 (-5+x) x \log ^2(10)+12 (-5+x)^2 x^2 \log ^4(10)+(-5+x)^3 x^3 \log ^6(10)+32 \exp \left (-\frac {4 \left (84-160 x \log ^2(10)-30 x^3 \log ^4(10)+3 x^4 \log ^4(10)+x^2 \log ^2(10) \left (32+75 \log ^2(10)\right )\right )}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2}\right ) x (-5+2 x) \log ^2(10) \left (5-5 x \log ^2(10)+x^2 \log ^2(10)\right )}{x \left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^3} \, dx\\ &=\int \left (\frac {64}{x \left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^3}+\frac {48 (-5+x) \log ^2(10)}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^3}+\frac {12 (-5+x)^2 x \log ^4(10)}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^3}+\frac {(-5+x)^3 x^2 \log ^6(10)}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^3}+\frac {32 \exp \left (-\frac {4 \left (84-160 x \log ^2(10)-30 x^3 \log ^4(10)+3 x^4 \log ^4(10)+x^2 \log ^2(10) \left (32+75 \log ^2(10)\right )\right )}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2}\right ) (5-2 x) \log ^2(10) \left (-5+5 x \log ^2(10)-x^2 \log ^2(10)\right )}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^3}\right ) \, dx\\ &=64 \int \frac {1}{x \left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^3} \, dx+\left (32 \log ^2(10)\right ) \int \frac {\exp \left (-\frac {4 \left (84-160 x \log ^2(10)-30 x^3 \log ^4(10)+3 x^4 \log ^4(10)+x^2 \log ^2(10) \left (32+75 \log ^2(10)\right )\right )}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2}\right ) (5-2 x) \left (-5+5 x \log ^2(10)-x^2 \log ^2(10)\right )}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^3} \, dx+\left (48 \log ^2(10)\right ) \int \frac {-5+x}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^3} \, dx+\left (12 \log ^4(10)\right ) \int \frac {(-5+x)^2 x}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^3} \, dx+\log ^6(10) \int \frac {(-5+x)^3 x^2}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^3} \, dx\\ &=-\frac {6 (5-x)^2 \log ^2(10) \left (8-5 x \log ^2(10)\right )}{\left (16-25 \log ^2(10)\right ) \left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2}-\frac {16 \left (8-25 \log ^2(10)+5 x \log ^2(10)\right )}{\left (16-25 \log ^2(10)\right ) \left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2}+\frac {(5-x)^3 \log ^4(10) \left (20+x \left (8-25 \log ^2(10)\right )\right )}{2 \left (16-25 \log ^2(10)\right ) \left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2}+\left (32 \log ^2(10)\right ) \int \left (\frac {\exp \left (-\frac {4 \left (84-160 x \log ^2(10)-30 x^3 \log ^4(10)+3 x^4 \log ^4(10)+x^2 \log ^2(10) \left (32+75 \log ^2(10)\right )\right )}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2}\right ) (-5+2 x)}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^3}+\frac {\exp \left (-\frac {4 \left (84-160 x \log ^2(10)-30 x^3 \log ^4(10)+3 x^4 \log ^4(10)+x^2 \log ^2(10) \left (32+75 \log ^2(10)\right )\right )}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2}\right ) (-5+2 x)}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2}\right ) \, dx+\frac {8 \int \frac {15 x \log ^4(10)+2 \log ^2(10) \left (16-25 \log ^2(10)\right )}{x \left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2} \, dx}{\log ^2(10) \left (16-25 \log ^2(10)\right )}+\frac {\left (6 \log ^2(10)\right ) \int \frac {(-5+x) \left (16-75 \log ^2(10)+5 x \log ^2(10)\right )}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2} \, dx}{16-25 \log ^2(10)}-\frac {\left (360 \log ^2(10)\right ) \int \frac {1}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2} \, dx}{16-25 \log ^2(10)}+\frac {\log ^4(10) \int \frac {(-5+x)^2 \left (5 \left (4-25 \log ^2(10)\right )+2 x \left (16-25 \log ^2(10)\right )\right )}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2} \, dx}{2 \left (16-25 \log ^2(10)\right )}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.37, size = 49, normalized size = 1.75 \begin {gather*} e^{-12-\frac {16}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2}-\frac {32}{4-5 x \log ^2(10)+x^2 \log ^2(10)}}+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(64 + (-240*x + 48*x^2)*Log[10]^2 + (300*x^2 - 120*x^3 + 12*x^4)*Log[10]^4 + (-125*x^3 + 75*x^4 - 15
*x^5 + x^6)*Log[10]^6 + E^((-336 + (640*x - 128*x^2)*Log[10]^2 + (-300*x^2 + 120*x^3 - 12*x^4)*Log[10]^4)/(16
+ (-40*x + 8*x^2)*Log[10]^2 + (25*x^2 - 10*x^3 + x^4)*Log[10]^4))*((-800*x + 320*x^2)*Log[10]^2 + (800*x^2 - 4
80*x^3 + 64*x^4)*Log[10]^4))/(64*x + (-240*x^2 + 48*x^3)*Log[10]^2 + (300*x^3 - 120*x^4 + 12*x^5)*Log[10]^4 +
(-125*x^4 + 75*x^5 - 15*x^6 + x^7)*Log[10]^6),x]

[Out]

E^(-12 - 16/(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2 - 32/(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)) + Log[x]

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fricas [B]  time = 0.77, size = 77, normalized size = 2.75 \begin {gather*} e^{\left (-\frac {4 \, {\left (3 \, {\left (x^{4} - 10 \, x^{3} + 25 \, x^{2}\right )} \log \left (10\right )^{4} + 32 \, {\left (x^{2} - 5 \, x\right )} \log \left (10\right )^{2} + 84\right )}}{{\left (x^{4} - 10 \, x^{3} + 25 \, x^{2}\right )} \log \left (10\right )^{4} + 8 \, {\left (x^{2} - 5 \, x\right )} \log \left (10\right )^{2} + 16}\right )} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x^4-480*x^3+800*x^2)*log(10)^4+(320*x^2-800*x)*log(10)^2)*exp(((-12*x^4+120*x^3-300*x^2)*log(1
0)^4+(-128*x^2+640*x)*log(10)^2-336)/((x^4-10*x^3+25*x^2)*log(10)^4+(8*x^2-40*x)*log(10)^2+16))+(x^6-15*x^5+75
*x^4-125*x^3)*log(10)^6+(12*x^4-120*x^3+300*x^2)*log(10)^4+(48*x^2-240*x)*log(10)^2+64)/((x^7-15*x^6+75*x^5-12
5*x^4)*log(10)^6+(12*x^5-120*x^4+300*x^3)*log(10)^4+(48*x^3-240*x^2)*log(10)^2+64*x),x, algorithm="fricas")

[Out]

e^(-4*(3*(x^4 - 10*x^3 + 25*x^2)*log(10)^4 + 32*(x^2 - 5*x)*log(10)^2 + 84)/((x^4 - 10*x^3 + 25*x^2)*log(10)^4
+ 8*(x^2 - 5*x)*log(10)^2 + 16)) + log(x)

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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((((64*x^4-480*x^3+800*x^2)*log(10)^4+(320*x^2-800*x)*log(10)^2)*exp(((-12*x^4+120*x^3-300*x^2)*log(1
0)^4+(-128*x^2+640*x)*log(10)^2-336)/((x^4-10*x^3+25*x^2)*log(10)^4+(8*x^2-40*x)*log(10)^2+16))+(x^6-15*x^5+75
*x^4-125*x^3)*log(10)^6+(12*x^4-120*x^3+300*x^2)*log(10)^4+(48*x^2-240*x)*log(10)^2+64)/((x^7-15*x^6+75*x^5-12
5*x^4)*log(10)^6+(12*x^5-120*x^4+300*x^3)*log(10)^4+(48*x^3-240*x^2)*log(10)^2+64*x),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 1.24, size = 155, normalized size = 5.54

method	result	size
risch	\(\ln \relax (x )+{\mathrm e}^{-\frac {4 \left (3 x^{2} \ln \relax (2)^{2}+6 x^{2} \ln \relax (2) \ln \relax (5)+3 x^{2} \ln \relax (5)^{2}-15 x \ln \relax (2)^{2}-30 x \ln \relax (2) \ln \relax (5)-15 x \ln \relax (5)^{2}+14\right ) \left (x^{2} \ln \relax (2)^{2}+2 x^{2} \ln \relax (2) \ln \relax (5)+x^{2} \ln \relax (5)^{2}-5 x \ln \relax (2)^{2}-10 x \ln \relax (2) \ln \relax (5)-5 x \ln \relax (5)^{2}+6\right )}{\left (x^{2} \ln \relax (2)^{2}+2 x^{2} \ln \relax (2) \ln \relax (5)+x^{2} \ln \relax (5)^{2}-5 x \ln \relax (2)^{2}-10 x \ln \relax (2) \ln \relax (5)-5 x \ln \relax (5)^{2}+4\right )^{2}}}\)	\(155\)
norman	\(\frac {\left (25 \ln \left (10\right )^{4}+8 \ln \left (10\right )^{2}\right ) x^{2} {\mathrm e}^{\frac {\left (-12 x^{4}+120 x^{3}-300 x^{2}\right ) \ln \left (10\right )^{4}+\left (-128 x^{2}+640 x \right ) \ln \left (10\right )^{2}-336}{\left (x^{4}-10 x^{3}+25 x^{2}\right ) \ln \left (10\right )^{4}+\left (8 x^{2}-40 x \right ) \ln \left (10\right )^{2}+16}}+\ln \left (10\right )^{4} x^{4} {\mathrm e}^{\frac {\left (-12 x^{4}+120 x^{3}-300 x^{2}\right ) \ln \left (10\right )^{4}+\left (-128 x^{2}+640 x \right ) \ln \left (10\right )^{2}-336}{\left (x^{4}-10 x^{3}+25 x^{2}\right ) \ln \left (10\right )^{4}+\left (8 x^{2}-40 x \right ) \ln \left (10\right )^{2}+16}}-40 \ln \left (10\right )^{2} x \,{\mathrm e}^{\frac {\left (-12 x^{4}+120 x^{3}-300 x^{2}\right ) \ln \left (10\right )^{4}+\left (-128 x^{2}+640 x \right ) \ln \left (10\right )^{2}-336}{\left (x^{4}-10 x^{3}+25 x^{2}\right ) \ln \left (10\right )^{4}+\left (8 x^{2}-40 x \right ) \ln \left (10\right )^{2}+16}}-10 \ln \left (10\right )^{4} x^{3} {\mathrm e}^{\frac {\left (-12 x^{4}+120 x^{3}-300 x^{2}\right ) \ln \left (10\right )^{4}+\left (-128 x^{2}+640 x \right ) \ln \left (10\right )^{2}-336}{\left (x^{4}-10 x^{3}+25 x^{2}\right ) \ln \left (10\right )^{4}+\left (8 x^{2}-40 x \right ) \ln \left (10\right )^{2}+16}}+16 \,{\mathrm e}^{\frac {\left (-12 x^{4}+120 x^{3}-300 x^{2}\right ) \ln \left (10\right )^{4}+\left (-128 x^{2}+640 x \right ) \ln \left (10\right )^{2}-336}{\left (x^{4}-10 x^{3}+25 x^{2}\right ) \ln \left (10\right )^{4}+\left (8 x^{2}-40 x \right ) \ln \left (10\right )^{2}+16}}}{\left (x^{2} \ln \left (10\right )^{2}-5 \ln \left (10\right )^{2} x +4\right )^{2}}+\ln \relax (x )\)	\(448\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((64*x^4-480*x^3+800*x^2)*ln(10)^4+(320*x^2-800*x)*ln(10)^2)*exp(((-12*x^4+120*x^3-300*x^2)*ln(10)^4+(-12
8*x^2+640*x)*ln(10)^2-336)/((x^4-10*x^3+25*x^2)*ln(10)^4+(8*x^2-40*x)*ln(10)^2+16))+(x^6-15*x^5+75*x^4-125*x^3
)*ln(10)^6+(12*x^4-120*x^3+300*x^2)*ln(10)^4+(48*x^2-240*x)*ln(10)^2+64)/((x^7-15*x^6+75*x^5-125*x^4)*ln(10)^6
+(12*x^5-120*x^4+300*x^3)*ln(10)^4+(48*x^3-240*x^2)*ln(10)^2+64*x),x,method=_RETURNVERBOSE)

[Out]

ln(x)+exp(-4*(3*x^2*ln(2)^2+6*x^2*ln(2)*ln(5)+3*x^2*ln(5)^2-15*x*ln(2)^2-30*x*ln(2)*ln(5)-15*x*ln(5)^2+14)*(x^
2*ln(2)^2+2*x^2*ln(2)*ln(5)+x^2*ln(5)^2-5*x*ln(2)^2-10*x*ln(2)*ln(5)-5*x*ln(5)^2+6)/(x^2*ln(2)^2+2*x^2*ln(2)*l
n(5)+x^2*ln(5)^2-5*x*ln(2)^2-10*x*ln(2)*ln(5)-5*x*ln(5)^2+4)^2)

________________________________________________________________________________________

maxima [B]  time = 5.66, size = 3013, normalized size = 107.61 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x^4-480*x^3+800*x^2)*log(10)^4+(320*x^2-800*x)*log(10)^2)*exp(((-12*x^4+120*x^3-300*x^2)*log(1
0)^4+(-128*x^2+640*x)*log(10)^2-336)/((x^4-10*x^3+25*x^2)*log(10)^4+(8*x^2-40*x)*log(10)^2+16))+(x^6-15*x^5+75
*x^4-125*x^3)*log(10)^6+(12*x^4-120*x^3+300*x^2)*log(10)^4+(48*x^2-240*x)*log(10)^2+64)/((x^7-15*x^6+75*x^5-12
5*x^4)*log(10)^6+(12*x^5-120*x^4+300*x^3)*log(10)^4+(48*x^3-240*x^2)*log(10)^2+64*x),x, algorithm="maxima")

[Out]

75/2*((120*x^3*log(10)^4 - (625*log(10)^6 + 100*log(10)^4 + 256*log(10)^2)*x^2 + 200*(5*log(10)^4 + 4*log(10)^
2)*x - 400*log(10)^2 - 512)/(10000*log(10)^8 - 12800*log(10)^6 + (625*log(10)^12 - 800*log(10)^10 + 256*log(10
)^8)*x^4 - 10*(625*log(10)^12 - 800*log(10)^10 + 256*log(10)^8)*x^3 + 4096*log(10)^4 + (15625*log(10)^12 - 150
00*log(10)^10 + 2048*log(10)^6)*x^2 - 40*(625*log(10)^10 - 800*log(10)^8 + 256*log(10)^6)*x) + 120*log((2*x*lo
g(10)^2 - 5*log(10)^2 - sqrt(25*log(10)^2 - 16)*log(10))/(2*x*log(10)^2 - 5*log(10)^2 + sqrt(25*log(10)^2 - 16
)*log(10)))/((625*log(10)^6 - 800*log(10)^4 + 256*log(10)^2)*sqrt(25*log(10)^2 - 16)*log(10)))*log(10)^6 - 1/2
*((500*(25*log(10)^8 - 30*log(10)^6 + 8*log(10)^4)*x^3 - 30000*log(10)^4 - (46875*log(10)^8 - 47500*log(10)^6
+ 4400*log(10)^4 + 2048*log(10)^2)*x^2 + 40*(1875*log(10)^6 - 2200*log(10)^4 + 496*log(10)^2)*x + 33600*log(10
)^2 - 6144)/(10000*log(10)^10 - 12800*log(10)^8 + 4096*log(10)^6 + (625*log(10)^14 - 800*log(10)^12 + 256*log(
10)^10)*x^4 - 10*(625*log(10)^14 - 800*log(10)^12 + 256*log(10)^10)*x^3 + (15625*log(10)^14 - 15000*log(10)^12
+ 2048*log(10)^8)*x^2 - 40*(625*log(10)^12 - 800*log(10)^10 + 256*log(10)^8)*x) - 25*(125*log(10)^4 - 200*log
(10)^2 + 96)*log((2*x*log(10)^2 - 5*log(10)^2 - sqrt(25*log(10)^2 - 16)*log(10))/(2*x*log(10)^2 - 5*log(10)^2
+ sqrt(25*log(10)^2 - 16)*log(10)))/((625*log(10)^8 - 800*log(10)^6 + 256*log(10)^4)*sqrt(25*log(10)^2 - 16)*l
og(10)) - log(x^2*log(10)^2 - 5*x*log(10)^2 + 4)/log(10)^6)*log(10)^6 + 15/2*((10*(125*log(10)^6 - 160*log(10)
^4 + 32*log(10)^2)*x^3 - 5*(625*log(10)^6 - 800*log(10)^4 - 32*log(10)^2)*x^2 + 8*(625*log(10)^4 - 1000*log(10
)^2 + 96)*x - 2000*log(10)^2 + 3200)/(10000*log(10)^8 - 12800*log(10)^6 + (625*log(10)^12 - 800*log(10)^10 + 2
56*log(10)^8)*x^4 - 10*(625*log(10)^12 - 800*log(10)^10 + 256*log(10)^8)*x^3 + 4096*log(10)^4 + (15625*log(10)
^12 - 15000*log(10)^10 + 2048*log(10)^6)*x^2 - 40*(625*log(10)^10 - 800*log(10)^8 + 256*log(10)^6)*x) - 192*lo
g((2*x*log(10)^2 - 5*log(10)^2 - sqrt(25*log(10)^2 - 16)*log(10))/(2*x*log(10)^2 - 5*log(10)^2 + sqrt(25*log(1
0)^2 - 16)*log(10)))/((625*log(10)^8 - 800*log(10)^6 + 256*log(10)^4)*sqrt(25*log(10)^2 - 16)*log(10)))*log(10
)^6 - 125/2*((2*(25*log(10)^4 + 8*log(10)^2)*x^3 - 15*(25*log(10)^4 + 8*log(10)^2)*x^2 + 8*(125*log(10)^2 - 8)
*x - 480)/(10000*log(10)^6 + (625*log(10)^10 - 800*log(10)^8 + 256*log(10)^6)*x^4 - 10*(625*log(10)^10 - 800*l
og(10)^8 + 256*log(10)^6)*x^3 - 12800*log(10)^4 + (15625*log(10)^10 - 15000*log(10)^8 + 2048*log(10)^4)*x^2 -
40*(625*log(10)^8 - 800*log(10)^6 + 256*log(10)^4)*x + 4096*log(10)^2) + 2*(25*log(10)^2 + 8)*log((2*x*log(10)
^2 - 5*log(10)^2 - sqrt(25*log(10)^2 - 16)*log(10))/(2*x*log(10)^2 - 5*log(10)^2 + sqrt(25*log(10)^2 - 16)*log
(10)))/((625*log(10)^6 - 800*log(10)^4 + 256*log(10)^2)*sqrt(25*log(10)^2 - 16)*log(10)))*log(10)^6 + 6*((120*
x^3*log(10)^4 - (625*log(10)^6 + 100*log(10)^4 + 256*log(10)^2)*x^2 + 200*(5*log(10)^4 + 4*log(10)^2)*x - 400*
log(10)^2 - 512)/(10000*log(10)^8 - 12800*log(10)^6 + (625*log(10)^12 - 800*log(10)^10 + 256*log(10)^8)*x^4 -
10*(625*log(10)^12 - 800*log(10)^10 + 256*log(10)^8)*x^3 + 4096*log(10)^4 + (15625*log(10)^12 - 15000*log(10)^
10 + 2048*log(10)^6)*x^2 - 40*(625*log(10)^10 - 800*log(10)^8 + 256*log(10)^6)*x) + 120*log((2*x*log(10)^2 - 5
*log(10)^2 - sqrt(25*log(10)^2 - 16)*log(10))/(2*x*log(10)^2 - 5*log(10)^2 + sqrt(25*log(10)^2 - 16)*log(10)))
/((625*log(10)^6 - 800*log(10)^4 + 256*log(10)^2)*sqrt(25*log(10)^2 - 16)*log(10)))*log(10)^4 + 150*((30*x^3*l
og(10)^4 - 225*x^2*log(10)^4 + 50*(5*log(10)^4 + 4*log(10)^2)*x - 100*log(10)^2 - 128)/(10000*log(10)^6 + (625
*log(10)^10 - 800*log(10)^8 + 256*log(10)^6)*x^4 - 10*(625*log(10)^10 - 800*log(10)^8 + 256*log(10)^6)*x^3 - 1
2800*log(10)^4 + (15625*log(10)^10 - 15000*log(10)^8 + 2048*log(10)^4)*x^2 - 40*(625*log(10)^8 - 800*log(10)^6
+ 256*log(10)^4)*x + 4096*log(10)^2) + 30*log((2*x*log(10)^2 - 5*log(10)^2 - sqrt(25*log(10)^2 - 16)*log(10))
/(2*x*log(10)^2 - 5*log(10)^2 + sqrt(25*log(10)^2 - 16)*log(10)))/((625*log(10)^4 - 800*log(10)^2 + 256)*sqrt(
25*log(10)^2 - 16)*log(10)))*log(10)^4 - 60*((2*(25*log(10)^4 + 8*log(10)^2)*x^3 - 15*(25*log(10)^4 + 8*log(10
)^2)*x^2 + 8*(125*log(10)^2 - 8)*x - 480)/(10000*log(10)^6 + (625*log(10)^10 - 800*log(10)^8 + 256*log(10)^6)*
x^4 - 10*(625*log(10)^10 - 800*log(10)^8 + 256*log(10)^6)*x^3 - 12800*log(10)^4 + (15625*log(10)^10 - 15000*lo
g(10)^8 + 2048*log(10)^4)*x^2 - 40*(625*log(10)^8 - 800*log(10)^6 + 256*log(10)^4)*x + 4096*log(10)^2) + 2*(25
*log(10)^2 + 8)*log((2*x*log(10)^2 - 5*log(10)^2 - sqrt(25*log(10)^2 - 16)*log(10))/(2*x*log(10)^2 - 5*log(10)
^2 + sqrt(25*log(10)^2 - 16)*log(10)))/((625*log(10)^6 - 800*log(10)^4 + 256*log(10)^2)*sqrt(25*log(10)^2 - 16
)*log(10)))*log(10)^4 + 24*((30*x^3*log(10)^4 - 225*x^2*log(10)^4 + 50*(5*log(10)^4 + 4*log(10)^2)*x - 100*log
(10)^2 - 128)/(10000*log(10)^6 + (625*log(10)^10 - 800*log(10)^8 + 256*log(10)^6)*x^4 - 10*(625*log(10)^10 - 8
00*log(10)^8 + 256*log(10)^6)*x^3 - 12800*log(10)^4 + (15625*log(10)^10 - 15000*log(10)^8 + 2048*log(10)^4)*x^
2 - 40*(625*log(10)^8 - 800*log(10)^6 + 256*log(10)^4)*x + 4096*log(10)^2) + 30*log((2*x*log(10)^2 - 5*log(10)
^2 - sqrt(25*log(10)^2 - 16)*log(10))/(2*x*log(10)^2 - 5*log(10)^2 + sqrt(25*log(10)^2 - 16)*log(10)))/((625*l
og(10)^4 - 800*log(10)^2 + 256)*sqrt(25*log(10)^2 - 16)*log(10)))*log(10)^2 - 120*((12*x^3*log(10)^2 - 90*x^2*
log(10)^2 + 20*(5*log(10)^2 + 4)*x + 125*log(10)^2 - 200)/((625*log(10)^8 - 800*log(10)^6 + 256*log(10)^4)*x^4
- 10*(625*log(10)^8 - 800*log(10)^6 + 256*log(10)^4)*x^3 + 10000*log(10)^4 + (15625*log(10)^8 - 15000*log(10)
^6 + 2048*log(10)^2)*x^2 - 40*(625*log(10)^6 - 800*log(10)^4 + 256*log(10)^2)*x - 12800*log(10)^2 + 4096) + 12
*log((2*x*log(10)^2 - 5*log(10)^2 - sqrt(25*log(10)^2 - 16)*log(10))/(2*x*log(10)^2 - 5*log(10)^2 + sqrt(25*lo
g(10)^2 - 16)*log(10)))/((625*log(10)^4 - 800*log(10)^2 + 256)*sqrt(25*log(10)^2 - 16)*log(10)))*log(10)^2 - 4
*(5*(25*log(10)^6 - 28*log(10)^4)*x^3 - 3750*log(10)^4 - 2*(625*log(10)^6 - 725*log(10)^4 + 64*log(10)^2)*x^2
+ 5*(625*log(10)^6 - 600*log(10)^4 - 16*log(10)^2)*x + 4200*log(10)^2 - 768)/((625*log(10)^8 - 800*log(10)^6 +
256*log(10)^4)*x^4 - 10*(625*log(10)^8 - 800*log(10)^6 + 256*log(10)^4)*x^3 + 10000*log(10)^4 + (15625*log(10
)^8 - 15000*log(10)^6 + 2048*log(10)^2)*x^2 - 40*(625*log(10)^6 - 800*log(10)^4 + 256*log(10)^2)*x - 12800*log
(10)^2 + 4096) + 25/2*(125*log(10)^6 - 200*log(10)^4 + 96*log(10)^2)*log((2*x*log(10)^2 - 5*log(10)^2 - sqrt(2
5*log(10)^2 - 16)*log(10))/(2*x*log(10)^2 - 5*log(10)^2 + sqrt(25*log(10)^2 - 16)*log(10)))/((625*log(10)^4 -
800*log(10)^2 + 256)*sqrt(25*log(10)^2 - 16)*log(10)) + e^(-16/((log(5)^4 + 4*log(5)^3*log(2) + 6*log(5)^2*log
(2)^2 + 4*log(5)*log(2)^3 + log(2)^4)*x^4 - 10*(log(5)^4 + 4*log(5)^3*log(2) + 6*log(5)^2*log(2)^2 + 4*log(5)*
log(2)^3 + log(2)^4)*x^3 + (25*log(5)^4 + 100*log(5)^3*log(2) + 25*log(2)^4 + 2*(75*log(2)^2 + 4)*log(5)^2 + 4
*(25*log(2)^3 + 4*log(2))*log(5) + 8*log(2)^2)*x^2 - 40*(log(5)^2 + 2*log(5)*log(2) + log(2)^2)*x + 16) - 32/(
(log(5)^2 + 2*log(5)*log(2) + log(2)^2)*x^2 - 5*(log(5)^2 + 2*log(5)*log(2) + log(2)^2)*x + 4) - 12) - 1/2*log
(x^2*log(10)^2 - 5*x*log(10)^2 + 4) + log(x)

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mupad [B]  time = 4.83, size = 331, normalized size = 11.82 \begin {gather*} \ln \relax (x)+{\mathrm {e}}^{-\frac {336}{8\,x^2\,{\ln \left (10\right )}^2+25\,x^2\,{\ln \left (10\right )}^4-10\,x^3\,{\ln \left (10\right )}^4+x^4\,{\ln \left (10\right )}^4-40\,x\,{\ln \left (10\right )}^2+16}}\,{\mathrm {e}}^{\frac {640\,x\,{\ln \left (10\right )}^2}{8\,x^2\,{\ln \left (10\right )}^2+25\,x^2\,{\ln \left (10\right )}^4-10\,x^3\,{\ln \left (10\right )}^4+x^4\,{\ln \left (10\right )}^4-40\,x\,{\ln \left (10\right )}^2+16}}\,{\mathrm {e}}^{-\frac {12\,x^4\,{\ln \left (10\right )}^4}{8\,x^2\,{\ln \left (10\right )}^2+25\,x^2\,{\ln \left (10\right )}^4-10\,x^3\,{\ln \left (10\right )}^4+x^4\,{\ln \left (10\right )}^4-40\,x\,{\ln \left (10\right )}^2+16}}\,{\mathrm {e}}^{\frac {120\,x^3\,{\ln \left (10\right )}^4}{8\,x^2\,{\ln \left (10\right )}^2+25\,x^2\,{\ln \left (10\right )}^4-10\,x^3\,{\ln \left (10\right )}^4+x^4\,{\ln \left (10\right )}^4-40\,x\,{\ln \left (10\right )}^2+16}}\,{\mathrm {e}}^{-\frac {128\,x^2\,{\ln \left (10\right )}^2}{8\,x^2\,{\ln \left (10\right )}^2+25\,x^2\,{\ln \left (10\right )}^4-10\,x^3\,{\ln \left (10\right )}^4+x^4\,{\ln \left (10\right )}^4-40\,x\,{\ln \left (10\right )}^2+16}}\,{\mathrm {e}}^{-\frac {300\,x^2\,{\ln \left (10\right )}^4}{8\,x^2\,{\ln \left (10\right )}^2+25\,x^2\,{\ln \left (10\right )}^4-10\,x^3\,{\ln \left (10\right )}^4+x^4\,{\ln \left (10\right )}^4-40\,x\,{\ln \left (10\right )}^2+16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(10)^4*(300*x^2 - 120*x^3 + 12*x^4) - log(10)^6*(125*x^3 - 75*x^4 + 15*x^5 - x^6) - log(10)^2*(240*x -
48*x^2) + exp(-(log(10)^4*(300*x^2 - 120*x^3 + 12*x^4) - log(10)^2*(640*x - 128*x^2) + 336)/(log(10)^4*(25*x^
2 - 10*x^3 + x^4) - log(10)^2*(40*x - 8*x^2) + 16))*(log(10)^4*(800*x^2 - 480*x^3 + 64*x^4) - log(10)^2*(800*x
- 320*x^2)) + 64)/(64*x + log(10)^4*(300*x^3 - 120*x^4 + 12*x^5) - log(10)^6*(125*x^4 - 75*x^5 + 15*x^6 - x^7
) - log(10)^2*(240*x^2 - 48*x^3)),x)

[Out]

log(x) + exp(-336/(8*x^2*log(10)^2 + 25*x^2*log(10)^4 - 10*x^3*log(10)^4 + x^4*log(10)^4 - 40*x*log(10)^2 + 16
))*exp((640*x*log(10)^2)/(8*x^2*log(10)^2 + 25*x^2*log(10)^4 - 10*x^3*log(10)^4 + x^4*log(10)^4 - 40*x*log(10)
^2 + 16))*exp(-(12*x^4*log(10)^4)/(8*x^2*log(10)^2 + 25*x^2*log(10)^4 - 10*x^3*log(10)^4 + x^4*log(10)^4 - 40*
x*log(10)^2 + 16))*exp((120*x^3*log(10)^4)/(8*x^2*log(10)^2 + 25*x^2*log(10)^4 - 10*x^3*log(10)^4 + x^4*log(10
)^4 - 40*x*log(10)^2 + 16))*exp(-(128*x^2*log(10)^2)/(8*x^2*log(10)^2 + 25*x^2*log(10)^4 - 10*x^3*log(10)^4 +
x^4*log(10)^4 - 40*x*log(10)^2 + 16))*exp(-(300*x^2*log(10)^4)/(8*x^2*log(10)^2 + 25*x^2*log(10)^4 - 10*x^3*lo
g(10)^4 + x^4*log(10)^4 - 40*x*log(10)^2 + 16))

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sympy [B]  time = 1.50, size = 73, normalized size = 2.61 \begin {gather*} e^{\frac {\left (- 128 x^{2} + 640 x\right ) \log {\left (10 \right )}^{2} + \left (- 12 x^{4} + 120 x^{3} - 300 x^{2}\right ) \log {\left (10 \right )}^{4} - 336}{\left (8 x^{2} - 40 x\right ) \log {\left (10 \right )}^{2} + \left (x^{4} - 10 x^{3} + 25 x^{2}\right ) \log {\left (10 \right )}^{4} + 16}} + \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((64*x**4-480*x**3+800*x**2)*ln(10)**4+(320*x**2-800*x)*ln(10)**2)*exp(((-12*x**4+120*x**3-300*x**2
)*ln(10)**4+(-128*x**2+640*x)*ln(10)**2-336)/((x**4-10*x**3+25*x**2)*ln(10)**4+(8*x**2-40*x)*ln(10)**2+16))+(x
**6-15*x**5+75*x**4-125*x**3)*ln(10)**6+(12*x**4-120*x**3+300*x**2)*ln(10)**4+(48*x**2-240*x)*ln(10)**2+64)/((
x**7-15*x**6+75*x**5-125*x**4)*ln(10)**6+(12*x**5-120*x**4+300*x**3)*ln(10)**4+(48*x**3-240*x**2)*ln(10)**2+64
*x),x)

[Out]

exp(((-128*x**2 + 640*x)*log(10)**2 + (-12*x**4 + 120*x**3 - 300*x**2)*log(10)**4 - 336)/((8*x**2 - 40*x)*log(
10)**2 + (x**4 - 10*x**3 + 25*x**2)*log(10)**4 + 16)) + log(x)

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