3.85.52 $\int \frac{(-1024x^4-1536x^5)\log (x)+e^4(-1024x^3-1536x^4){\log }^2(x)+e^8(-384x^2-576x^3){\log }^3(x)+e^{12}(-64x-96x^2){\log }^4(x)+e^{16}(-4-6x){\log }^5(x)+(-2048x^4-3072x^5+(-768x^5+e^4(-1536x^3-2304x^4))\log (x)+(e^8(-384x^2-576x^3)+e^4(-512x^3-1536x^4)){\log }^2(x)+(e^{12}(-32x-48x^2)+e^8(-384x^2-864x^3)){\log }^3(x)+e^{12}(-96x-192x^2){\log }^4(x)+e^{16}(-8-15x){\log }^5(x))\log (x^2)}{(8x^5+24x^6+18x^7){\log }^5(x){\log }^2(x^2)}dx$

Optimal. Leaf size=30 $$\frac{{(\frac{e^4}{x}+\frac{4}{\log (x)})}^4}{(4+6x)\log \left(x^2\right)}$$

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Rubi [F]  time = 32.68, 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 = {} $$\begin{array}{c}\int \frac{(-1024x^4-1536x^5)\log (x)+e^4(-1024x^3-1536x^4){\log }^2(x)+e^8(-384x^2-576x^3){\log }^3(x)+e^{12}(-64x-96x^2){\log }^4(x)+e^{16}(-4-6x){\log }^5(x)+(-2048x^4-3072x^5+(-768x^5+e^4(-1536x^3-2304x^4))\log (x)+(e^8(-384x^2-576x^3)+e^4(-512x^3-1536x^4)){\log }^2(x)+(e^{12}(-32x-48x^2)+e^8(-384x^2-864x^3)){\log }^3(x)+e^{12}(-96x-192x^2){\log }^4(x)+e^{16}(-8-15x){\log }^5(x))\log \left(x^2\right)}{(8x^5+24x^6+18x^7){\log }^5(x){\log }^2\left(x^2\right)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[((-1024*x^4 - 1536*x^5)*Log[x] + E^4*(-1024*x^3 - 1536*x^4)*Log[x]^2 + E^8*(-384*x^2 - 576*x^3)*Log[x]^3 +
E^12*(-64*x - 96*x^2)*Log[x]^4 + E^16*(-4 - 6*x)*Log[x]^5 + (-2048*x^4 - 3072*x^5 + (-768*x^5 + E^4*(-1536*x^
3 - 2304*x^4))*Log[x] + (E^8*(-384*x^2 - 576*x^3) + E^4*(-512*x^3 - 1536*x^4))*Log[x]^2 + (E^12*(-32*x - 48*x^
2) + E^8*(-384*x^2 - 864*x^3))*Log[x]^3 + E^12*(-96*x - 192*x^2)*Log[x]^4 + E^16*(-8 - 15*x)*Log[x]^5)*Log[x^2
])/((8*x^5 + 24*x^6 + 18*x^7)*Log[x]^5*Log[x^2]^2),x]

[Out]

(-6075*E^16*x*ExpIntegralEi[Log[x^2]/2])/(256*Sqrt[x^2]) + (81*E^16)/(64*Log[x^2]) + E^16/(4*x^4*Log[x^2]) - (
3*E^16)/(8*x^3*Log[x^2]) + (9*E^16)/(16*x^2*Log[x^2]) - (27*E^16)/(32*x*Log[x^2]) + (243*E^16*Defer[Int][1/((2
+ 3*x)*Log[x^2]^2), x])/32 - 128*Defer[Int][1/(x*Log[x]^4*Log[x^2]^2), x] + 384*Defer[Int][1/((2 + 3*x)*Log[x
]^4*Log[x^2]^2), x] - 128*E^4*Defer[Int][1/(x^2*Log[x]^3*Log[x^2]^2), x] + 192*E^4*Defer[Int][1/(x*Log[x]^3*Lo
g[x^2]^2), x] - 576*E^4*Defer[Int][1/((2 + 3*x)*Log[x]^3*Log[x^2]^2), x] - 48*E^8*Defer[Int][1/(x^3*Log[x]^2*L
og[x^2]^2), x] + 72*E^8*Defer[Int][1/(x^2*Log[x]^2*Log[x^2]^2), x] - 108*E^8*Defer[Int][1/(x*Log[x]^2*Log[x^2]
^2), x] + 324*E^8*Defer[Int][1/((2 + 3*x)*Log[x]^2*Log[x^2]^2), x] - 8*E^12*Defer[Int][1/(x^4*Log[x]*Log[x^2]^
2), x] + 12*E^12*Defer[Int][1/(x^3*Log[x]*Log[x^2]^2), x] - 18*E^12*Defer[Int][1/(x^2*Log[x]*Log[x^2]^2), x] +
27*E^12*Defer[Int][1/(x*Log[x]*Log[x^2]^2), x] - 81*E^12*Defer[Int][1/((2 + 3*x)*Log[x]*Log[x^2]^2), x] + (24
3*E^16*Defer[Int][1/((2 + 3*x)^2*Log[x^2]), x])/8 + (3645*E^16*Defer[Int][x/((2 + 3*x)^2*Log[x^2]), x])/64 + (
1215*E^16*Defer[Int][1/((2 + 3*x)*Log[x^2]), x])/16 + (18225*E^16*Defer[Int][x/((2 + 3*x)*Log[x^2]), x])/128 -
256*Defer[Int][1/(x*Log[x]^5*Log[x^2]), x] + 768*Defer[Int][1/((2 + 3*x)*Log[x]^5*Log[x^2]), x] - 192*E^4*Def
er[Int][1/(x^2*Log[x]^4*Log[x^2]), x] + 288*E^4*Defer[Int][1/(x*Log[x]^4*Log[x^2]), x] - 384*Defer[Int][1/((2
+ 3*x)^2*Log[x]^4*Log[x^2]), x] - 864*E^4*Defer[Int][1/((2 + 3*x)*Log[x]^4*Log[x^2]), x] - 48*E^8*Defer[Int][1
/(x^3*Log[x]^3*Log[x^2]), x] + 144*E^8*Defer[Int][1/(x^2*Log[x]^3*Log[x^2]), x] - 8*E^4*(8 + 9*E^4)*Defer[Int]
[1/(x^2*Log[x]^3*Log[x^2]), x] - 192*E^4*Defer[Int][1/(x*Log[x]^3*Log[x^2]), x] - 324*E^8*Defer[Int][1/(x*Log[
x]^3*Log[x^2]), x] + 24*E^4*(8 + 9*E^4)*Defer[Int][1/(x*Log[x]^3*Log[x^2]), x] + 1152*E^4*Defer[Int][1/((2 + 3
*x)^2*Log[x]^3*Log[x^2]), x] + 648*E^8*Defer[Int][1/((2 + 3*x)^2*Log[x]^3*Log[x^2]), x] - 72*E^4*(8 + 9*E^4)*D
efer[Int][1/((2 + 3*x)^2*Log[x]^3*Log[x^2]), x] + 576*E^4*Defer[Int][1/((2 + 3*x)*Log[x]^3*Log[x^2]), x] + 972
*E^8*Defer[Int][1/((2 + 3*x)*Log[x]^3*Log[x^2]), x] - 72*E^4*(8 + 9*E^4)*Defer[Int][1/((2 + 3*x)*Log[x]^3*Log[
x^2]), x] - 4*E^12*Defer[Int][1/(x^4*Log[x]^2*Log[x^2]), x] + 12*E^12*Defer[Int][1/(x^3*Log[x]^2*Log[x^2]), x]
- 6*E^8*(8 + E^4)*Defer[Int][1/(x^3*Log[x]^2*Log[x^2]), x] - 108*E^8*Defer[Int][1/(x^2*Log[x]^2*Log[x^2]), x]
- 27*E^12*Defer[Int][1/(x^2*Log[x]^2*Log[x^2]), x] + 18*E^8*(8 + E^4)*Defer[Int][1/(x^2*Log[x]^2*Log[x^2]), x
] + 324*E^8*Defer[Int][1/(x*Log[x]^2*Log[x^2]), x] + 54*E^12*Defer[Int][1/(x*Log[x]^2*Log[x^2]), x] - (81*E^8*
(8 + E^4)*Defer[Int][1/(x*Log[x]^2*Log[x^2]), x])/2 - 972*E^8*Defer[Int][1/((2 + 3*x)^2*Log[x]^2*Log[x^2]), x]
- 81*E^12*Defer[Int][1/((2 + 3*x)^2*Log[x]^2*Log[x^2]), x] + 81*E^8*(8 + E^4)*Defer[Int][1/((2 + 3*x)^2*Log[x
]^2*Log[x^2]), x] - 972*E^8*Defer[Int][1/((2 + 3*x)*Log[x]^2*Log[x^2]), x] - 162*E^12*Defer[Int][1/((2 + 3*x)*
Log[x]^2*Log[x^2]), x] + (243*E^8*(8 + E^4)*Defer[Int][1/((2 + 3*x)*Log[x]^2*Log[x^2]), x])/2 - 12*E^12*Defer[
Int][1/(x^4*Log[x]*Log[x^2]), x] + 12*E^12*Defer[Int][1/(x^3*Log[x]*Log[x^2]), x] - 9*E^12*Defer[Int][1/(x^2*L
og[x]*Log[x^2]), x] + 81*E^12*Defer[Int][1/((2 + 3*x)^2*Log[x]*Log[x^2]), x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{(-1024x^4-1536x^5)\log (x)+e^4(-1024x^3-1536x^4){\log }^2(x)+e^8(-384x^2-576x^3){\log }^3(x)+e^{12}(-64x-96x^2){\log }^4(x)+e^{16}(-4-6x){\log }^5(x)+(-2048x^4-3072x^5+(-768x^5+e^4(-1536x^3-2304x^4))\log (x)+(e^8(-384x^2-576x^3)+e^4(-512x^3-1536x^4)){\log }^2(x)+(e^{12}(-32x-48x^2)+e^8(-384x^2-864x^3)){\log }^3(x)+e^{12}(-96x-192x^2){\log }^4(x)+e^{16}(-8-15x){\log }^5(x))\log \left(x^2\right)}{x^5(8+24x+18x^2){\log }^5(x){\log }^2\left(x^2\right)}dx\\ & =\int \frac{(-1024x^4-1536x^5)\log (x)+e^4(-1024x^3-1536x^4){\log }^2(x)+e^8(-384x^2-576x^3){\log }^3(x)+e^{12}(-64x-96x^2){\log }^4(x)+e^{16}(-4-6x){\log }^5(x)+(-2048x^4-3072x^5+(-768x^5+e^4(-1536x^3-2304x^4))\log (x)+(e^8(-384x^2-576x^3)+e^4(-512x^3-1536x^4)){\log }^2(x)+(e^{12}(-32x-48x^2)+e^8(-384x^2-864x^3)){\log }^3(x)+e^{12}(-96x-192x^2){\log }^4(x)+e^{16}(-8-15x){\log }^5(x))\log \left(x^2\right)}{2x^5(2+3x{)}^2{\log }^5(x){\log }^2\left(x^2\right)}dx\\ & =\frac{1}{2}\int \frac{(-1024x^4-1536x^5)\log (x)+e^4(-1024x^3-1536x^4){\log }^2(x)+e^8(-384x^2-576x^3){\log }^3(x)+e^{12}(-64x-96x^2){\log }^4(x)+e^{16}(-4-6x){\log }^5(x)+(-2048x^4-3072x^5+(-768x^5+e^4(-1536x^3-2304x^4))\log (x)+(e^8(-384x^2-576x^3)+e^4(-512x^3-1536x^4)){\log }^2(x)+(e^{12}(-32x-48x^2)+e^8(-384x^2-864x^3)){\log }^3(x)+e^{12}(-96x-192x^2){\log }^4(x)+e^{16}(-8-15x){\log }^5(x))\log \left(x^2\right)}{x^5(2+3x{)}^2{\log }^5(x){\log }^2\left(x^2\right)}dx\\ & =\frac{1}{2}\int \frac{{(4x+e^4\log (x))}^3(-16x(2+3x)\log \left(x^2\right)-4x\log (x)(4+6x+3x\log \left(x^2\right))-e^4{\log }^2(x)(4+6x+(8+15x)\log \left(x^2\right)))}{x^5(2+3x{)}^2{\log }^5(x){\log }^2\left(x^2\right)}dx\\ & =\frac{1}{2}\int (-\frac{2{(4x+e^4\log (x))}^4}{x^5(2+3x){\log }^4(x){\log }^2\left(x^2\right)}-\frac{{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{x^5(2+3x{)}^2{\log }^5(x)\log \left(x^2\right)})dx\\ & =-(\frac{1}{2}\int \frac{{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{x^5(2+3x{)}^2{\log }^5(x)\log \left(x^2\right)}dx)-\int \frac{{(4x+e^4\log (x))}^4}{x^5(2+3x){\log }^4(x){\log }^2\left(x^2\right)}dx\\ & =-(\frac{1}{2}\int (\frac{{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{4x^5{\log }^5(x)\log \left(x^2\right)}-\frac{3{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{4x^4{\log }^5(x)\log \left(x^2\right)}+\frac{27{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{16x^3{\log }^5(x)\log \left(x^2\right)}-\frac{27{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{8x^2{\log }^5(x)\log \left(x^2\right)}+\frac{405{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{64x{\log }^5(x)\log \left(x^2\right)}-\frac{243{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{32(2+3x{)}^2{\log }^5(x)\log \left(x^2\right)}-\frac{1215{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{64(2+3x){\log }^5(x)\log \left(x^2\right)})dx)-\int (\frac{{(4x+e^4\log (x))}^4}{2x^5{\log }^4(x){\log }^2\left(x^2\right)}-\frac{3{(4x+e^4\log (x))}^4}{4x^4{\log }^4(x){\log }^2\left(x^2\right)}+\frac{9{(4x+e^4\log (x))}^4}{8x^3{\log }^4(x){\log }^2\left(x^2\right)}-\frac{27{(4x+e^4\log (x))}^4}{16x^2{\log }^4(x){\log }^2\left(x^2\right)}+\frac{81{(4x+e^4\log (x))}^4}{32x{\log }^4(x){\log }^2\left(x^2\right)}-\frac{243{(4x+e^4\log (x))}^4}{32(2+3x){\log }^4(x){\log }^2\left(x^2\right)})dx\\ & =-(\frac{1}{8}\int \frac{{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{x^5{\log }^5(x)\log \left(x^2\right)}dx)+\frac{3}{8}\int \frac{{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{x^4{\log }^5(x)\log \left(x^2\right)}dx-\frac{1}{2}\int \frac{{(4x+e^4\log (x))}^4}{x^5{\log }^4(x){\log }^2\left(x^2\right)}dx+\frac{3}{4}\int \frac{{(4x+e^4\log (x))}^4}{x^4{\log }^4(x){\log }^2\left(x^2\right)}dx-\frac{27}{32}\int \frac{{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{x^3{\log }^5(x)\log \left(x^2\right)}dx-\frac{9}{8}\int \frac{{(4x+e^4\log (x))}^4}{x^3{\log }^4(x){\log }^2\left(x^2\right)}dx+\frac{27}{16}\int \frac{{(4x+e^4\log (x))}^4}{x^2{\log }^4(x){\log }^2\left(x^2\right)}dx+\frac{27}{16}\int \frac{{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{x^2{\log }^5(x)\log \left(x^2\right)}dx-\frac{81}{32}\int \frac{{(4x+e^4\log (x))}^4}{x{\log }^4(x){\log }^2\left(x^2\right)}dx-\frac{405}{128}\int \frac{{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{x{\log }^5(x)\log \left(x^2\right)}dx+\frac{243}{64}\int \frac{{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{(2+3x{)}^2{\log }^5(x)\log \left(x^2\right)}dx+\frac{243}{32}\int \frac{{(4x+e^4\log (x))}^4}{(2+3x){\log }^4(x){\log }^2\left(x^2\right)}dx+\frac{1215}{128}\int \frac{{(4x+e^4\log (x))}^3(32x+48x^2+12x^2\log (x)+8e^4{\log }^2(x)+15e^{4}x{\log }^2(x))}{(2+3x){\log }^5(x)\log \left(x^2\right)}dx\\ & =\text{Rest of rules removed due to large latex content}\end{array}\end{array}$$

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Mathematica [A]  time = 0.26, size = 36, normalized size = 1.20 $$\begin{array}{c}\frac{{(4x+e^4\log (x))}^4}{2x^4(2+3x){\log }^4(x)\log \left(x^2\right)}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[((-1024*x^4 - 1536*x^5)*Log[x] + E^4*(-1024*x^3 - 1536*x^4)*Log[x]^2 + E^8*(-384*x^2 - 576*x^3)*Log[
x]^3 + E^12*(-64*x - 96*x^2)*Log[x]^4 + E^16*(-4 - 6*x)*Log[x]^5 + (-2048*x^4 - 3072*x^5 + (-768*x^5 + E^4*(-1
536*x^3 - 2304*x^4))*Log[x] + (E^8*(-384*x^2 - 576*x^3) + E^4*(-512*x^3 - 1536*x^4))*Log[x]^2 + (E^12*(-32*x -
48*x^2) + E^8*(-384*x^2 - 864*x^3))*Log[x]^3 + E^12*(-96*x - 192*x^2)*Log[x]^4 + E^16*(-8 - 15*x)*Log[x]^5)*L
og[x^2])/((8*x^5 + 24*x^6 + 18*x^7)*Log[x]^5*Log[x^2]^2),x]

[Out]

(4*x + E^4*Log[x])^4/(2*x^4*(2 + 3*x)*Log[x]^4*Log[x^2])

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fricas [B]  time = 0.97, size = 61, normalized size = 2.03 $$\begin{array}{c}\frac{256x^3{e}^4\log (x)+96x^2{e}^8\log (x{)}^2+16x{e}^{12}\log (x{)}^3+e^{16}\log (x{)}^4+256x^4}{4(3x^5+2x^4)\log (x{)}^5}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-15*x-8)*exp(4)^4*log(x)^5+(-192*x^2-96*x)*exp(4)^3*log(x)^4+((-48*x^2-32*x)*exp(4)^3+(-864*x^3-3
84*x^2)*exp(4)^2)*log(x)^3+((-576*x^3-384*x^2)*exp(4)^2+(-1536*x^4-512*x^3)*exp(4))*log(x)^2+((-2304*x^4-1536*
x^3)*exp(4)-768*x^5)*log(x)-3072*x^5-2048*x^4)*log(x^2)+(-6*x-4)*exp(4)^4*log(x)^5+(-96*x^2-64*x)*exp(4)^3*log
(x)^4+(-576*x^3-384*x^2)*exp(4)^2*log(x)^3+(-1536*x^4-1024*x^3)*exp(4)*log(x)^2+(-1536*x^5-1024*x^4)*log(x))/(
18*x^7+24*x^6+8*x^5)/log(x)^5/log(x^2)^2,x, algorithm="fricas")

[Out]

1/4*(256*x^3*e^4*log(x) + 96*x^2*e^8*log(x)^2 + 16*x*e^12*log(x)^3 + e^16*log(x)^4 + 256*x^4)/((3*x^5 + 2*x^4)
*log(x)^5)

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giac [B]  time = 0.33, size = 65, normalized size = 2.17 $$\begin{array}{c}\frac{256x^3{e}^4\log (x)+96x^2{e}^8\log (x{)}^2+16x{e}^{12}\log (x{)}^3+e^{16}\log (x{)}^4+256x^4}{4(3x^5\log (x{)}^5+2x^4\log (x{)}^5)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-15*x-8)*exp(4)^4*log(x)^5+(-192*x^2-96*x)*exp(4)^3*log(x)^4+((-48*x^2-32*x)*exp(4)^3+(-864*x^3-3
84*x^2)*exp(4)^2)*log(x)^3+((-576*x^3-384*x^2)*exp(4)^2+(-1536*x^4-512*x^3)*exp(4))*log(x)^2+((-2304*x^4-1536*
x^3)*exp(4)-768*x^5)*log(x)-3072*x^5-2048*x^4)*log(x^2)+(-6*x-4)*exp(4)^4*log(x)^5+(-96*x^2-64*x)*exp(4)^3*log
(x)^4+(-576*x^3-384*x^2)*exp(4)^2*log(x)^3+(-1536*x^4-1024*x^3)*exp(4)*log(x)^2+(-1536*x^5-1024*x^4)*log(x))/(
18*x^7+24*x^6+8*x^5)/log(x)^5/log(x^2)^2,x, algorithm="giac")

[Out]

1/4*(256*x^3*e^4*log(x) + 96*x^2*e^8*log(x)^2 + 16*x*e^12*log(x)^3 + e^16*log(x)^4 + 256*x^4)/(3*x^5*log(x)^5
+ 2*x^4*log(x)^5)

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maple [C]  time = 0.72, size = 114, normalized size = 3.80

method	result	size
risch	$\frac{{\mathrm{e}}^{16}\ln (x{)}^4+16{\mathrm{e}}^{12}x\ln (x{)}^3+96{\mathrm{e}}^8{x}^2\ln (x{)}^2+256{\mathrm{e}}^4{x}^3\ln (x)+256x^4}{\ln (x{)}^4(-i\pi \mathrm{csgn}{\left(ix\right)}^2\mathrm{csgn}\left(i{x}^2\right)+2i\pi \mathrm{csgn}\left(ix\right)\mathrm{csgn}{\left(i{x}^2\right)}^2-i\pi \mathrm{csgn}{\left(i{x}^2\right)}^3+4\ln (x))x^4(3x+2)}$	$114$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-15*x-8)*exp(4)^4*ln(x)^5+(-192*x^2-96*x)*exp(4)^3*ln(x)^4+((-48*x^2-32*x)*exp(4)^3+(-864*x^3-384*x^2)*
exp(4)^2)*ln(x)^3+((-576*x^3-384*x^2)*exp(4)^2+(-1536*x^4-512*x^3)*exp(4))*ln(x)^2+((-2304*x^4-1536*x^3)*exp(4
)-768*x^5)*ln(x)-3072*x^5-2048*x^4)*ln(x^2)+(-6*x-4)*exp(4)^4*ln(x)^5+(-96*x^2-64*x)*exp(4)^3*ln(x)^4+(-576*x^
3-384*x^2)*exp(4)^2*ln(x)^3+(-1536*x^4-1024*x^3)*exp(4)*ln(x)^2+(-1536*x^5-1024*x^4)*ln(x))/(18*x^7+24*x^6+8*x
^5)/ln(x)^5/ln(x^2)^2,x,method=_RETURNVERBOSE)

[Out]

(exp(16)*ln(x)^4+16*exp(12)*x*ln(x)^3+96*exp(8)*x^2*ln(x)^2+256*exp(4)*x^3*ln(x)+256*x^4)/ln(x)^4/(-I*Pi*csgn(
I*x)^2*csgn(I*x^2)+2*I*Pi*csgn(I*x)*csgn(I*x^2)^2-I*Pi*csgn(I*x^2)^3+4*ln(x))/x^4/(3*x+2)

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maxima [B]  time = 0.47, size = 61, normalized size = 2.03 $$\begin{array}{c}\frac{256x^3{e}^4\log (x)+96x^2{e}^8\log (x{)}^2+16x{e}^{12}\log (x{)}^3+e^{16}\log (x{)}^4+256x^4}{4(3x^5+2x^4)\log (x{)}^5}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-15*x-8)*exp(4)^4*log(x)^5+(-192*x^2-96*x)*exp(4)^3*log(x)^4+((-48*x^2-32*x)*exp(4)^3+(-864*x^3-3
84*x^2)*exp(4)^2)*log(x)^3+((-576*x^3-384*x^2)*exp(4)^2+(-1536*x^4-512*x^3)*exp(4))*log(x)^2+((-2304*x^4-1536*
x^3)*exp(4)-768*x^5)*log(x)-3072*x^5-2048*x^4)*log(x^2)+(-6*x-4)*exp(4)^4*log(x)^5+(-96*x^2-64*x)*exp(4)^3*log
(x)^4+(-576*x^3-384*x^2)*exp(4)^2*log(x)^3+(-1536*x^4-1024*x^3)*exp(4)*log(x)^2+(-1536*x^5-1024*x^4)*log(x))/(
18*x^7+24*x^6+8*x^5)/log(x)^5/log(x^2)^2,x, algorithm="maxima")

[Out]

1/4*(256*x^3*e^4*log(x) + 96*x^2*e^8*log(x)^2 + 16*x*e^12*log(x)^3 + e^16*log(x)^4 + 256*x^4)/((3*x^5 + 2*x^4)
*log(x)^5)

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mupad [B]  time = 6.45, size = 892, normalized size = 29.73 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x)*(1024*x^4 + 1536*x^5) + log(x^2)*(log(x)^2*(exp(8)*(384*x^2 + 576*x^3) + exp(4)*(512*x^3 + 1536*x
^4)) + log(x)*(exp(4)*(1536*x^3 + 2304*x^4) + 768*x^5) + log(x)^3*(exp(12)*(32*x + 48*x^2) + exp(8)*(384*x^2 +
864*x^3)) + 2048*x^4 + 3072*x^5 + exp(16)*log(x)^5*(15*x + 8) + exp(12)*log(x)^4*(96*x + 192*x^2)) + exp(16)*
log(x)^5*(6*x + 4) + exp(12)*log(x)^4*(64*x + 96*x^2) + exp(8)*log(x)^3*(384*x^2 + 576*x^3) + exp(4)*log(x)^2*
(1024*x^3 + 1536*x^4))/(log(x^2)^2*log(x)^5*(8*x^5 + 24*x^6 + 18*x^7)),x)

[Out]

((4*exp(16)*(log(x^2) - 2*log(x))^4 + 8*exp(16)*(log(x^2) - 2*log(x))^5 + 12288*x^5*(log(x^2) - 2*log(x)) + 16
384*x^4 + 24576*x^5 - 8192*x^3*exp(4)*(log(x^2) - 2*log(x)) - 12288*x^4*exp(4)*(log(x^2) - 2*log(x)) - 128*x*e
xp(12)*(log(x^2) - 2*log(x))^3 - 192*x*exp(12)*(log(x^2) - 2*log(x))^4 + 6*x*exp(16)*(log(x^2) - 2*log(x))^4 +
15*x*exp(16)*(log(x^2) - 2*log(x))^5 - 4096*x^3*exp(4)*(log(x^2) - 2*log(x))^2 - 12288*x^4*exp(4)*(log(x^2) -
2*log(x))^2 + 1536*x^2*exp(8)*(log(x^2) - 2*log(x))^2 + 1536*x^2*exp(8)*(log(x^2) - 2*log(x))^3 + 2304*x^3*ex
p(8)*(log(x^2) - 2*log(x))^2 + 3456*x^3*exp(8)*(log(x^2) - 2*log(x))^3 - 192*x^2*exp(12)*(log(x^2) - 2*log(x))
^3 - 384*x^2*exp(12)*(log(x^2) - 2*log(x))^4)/(4*x^4*(3*x + 2)^2*(log(x^2) - 2*log(x))^4) + (log(x)*(8*exp(16)
*(log(x^2) - 2*log(x))^4 + 12288*x^5 - 4096*x^3*exp(4)*(log(x^2) - 2*log(x)) - 12288*x^4*exp(4)*(log(x^2) - 2*
log(x)) - 192*x*exp(12)*(log(x^2) - 2*log(x))^3 + 15*x*exp(16)*(log(x^2) - 2*log(x))^4 + 1536*x^2*exp(8)*(log(
x^2) - 2*log(x))^2 + 3456*x^3*exp(8)*(log(x^2) - 2*log(x))^2 - 384*x^2*exp(12)*(log(x^2) - 2*log(x))^3))/(2*x^
4*(3*x + 2)^2*(log(x^2) - 2*log(x))^4))/log(x^2) - (8*exp(16)*(log(x^2) - 2*log(x))^4 - x*(192*exp(12)*(log(x^
2) - 2*log(x))^3 - 15*exp(16)*(log(x^2) - 2*log(x))^4) + x^3*(3456*exp(8)*(log(x^2) - 2*log(x))^2 - 4096*exp(4
)*(log(x^2) - 2*log(x))) + x^2*(1536*exp(8)*(log(x^2) - 2*log(x))^2 - 384*exp(12)*(log(x^2) - 2*log(x))^3) + 1
2288*x^5 - 12288*x^4*exp(4)*(log(x^2) - 2*log(x)))/(16*x^4*(log(x^2) - 2*log(x))^4 + 48*x^5*(log(x^2) - 2*log(
x))^4 + 36*x^6*(log(x^2) - 2*log(x))^4) + 128/(log(x)^4*(3*x + 2)*(log(x^2) - 2*log(x))) + (8*(exp(12)*(log(x^
2) - 2*log(x))^3 - 128*x^3 + 64*x^2*exp(4)*(log(x^2) - 2*log(x)) - 12*x*exp(8)*(log(x^2) - 2*log(x))^2))/(x^3*
log(x)*(3*x + 2)*(log(x^2) - 2*log(x))^4) + (16*(3*exp(8)*(log(x^2) - 2*log(x))^2 + 32*x^2 - 16*x*exp(4)*(log(
x^2) - 2*log(x))))/(x^2*log(x)^2*(3*x + 2)*(log(x^2) - 2*log(x))^3) - (128*(2*x - exp(4)*(log(x^2) - 2*log(x))
))/(x*log(x)^3*(3*x + 2)*(log(x^2) - 2*log(x))^2)

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sympy [B]  time = 0.47, size = 65, normalized size = 2.17 $$\begin{array}{c}\frac{256x^4+256x^3{e}^4\log (x)+96x^2{e}^8\log {(x)}^2+16x{e}^{12}\log {(x)}^3+e^{16}\log {(x)}^4}{(12x^5+8x^4)\log {(x)}^5}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-15*x-8)*exp(4)**4*ln(x)**5+(-192*x**2-96*x)*exp(4)**3*ln(x)**4+((-48*x**2-32*x)*exp(4)**3+(-864*
x**3-384*x**2)*exp(4)**2)*ln(x)**3+((-576*x**3-384*x**2)*exp(4)**2+(-1536*x**4-512*x**3)*exp(4))*ln(x)**2+((-2
304*x**4-1536*x**3)*exp(4)-768*x**5)*ln(x)-3072*x**5-2048*x**4)*ln(x**2)+(-6*x-4)*exp(4)**4*ln(x)**5+(-96*x**2
-64*x)*exp(4)**3*ln(x)**4+(-576*x**3-384*x**2)*exp(4)**2*ln(x)**3+(-1536*x**4-1024*x**3)*exp(4)*ln(x)**2+(-153
6*x**5-1024*x**4)*ln(x))/(18*x**7+24*x**6+8*x**5)/ln(x)**5/ln(x**2)**2,x)

[Out]

(256*x**4 + 256*x**3*exp(4)*log(x) + 96*x**2*exp(8)*log(x)**2 + 16*x*exp(12)*log(x)**3 + exp(16)*log(x)**4)/((
12*x**5 + 8*x**4)*log(x)**5)

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