3.9.90 \(\int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} (16-8 x^2+x^4)+e^{12} (-64 x+32 x^3-4 x^5)+e^8 (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6)+e^4 (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7)+(32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} (-64+32 x^2-4 x^4)+e^8 (192 x-96 x^3+12 x^5)+e^4 (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6)) \log (x)+(16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 (96-48 x^2+6 x^4)+e^4 (-192 x+96 x^3-12 x^5)) \log ^2(x)+(64 x-32 x^3+4 x^5+e^4 (-64+32 x^2-4 x^4)) \log ^3(x)+(16-8 x^2+x^4) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} (16-8 x^2+x^4)+e^{12} (-64 x+32 x^3-4 x^5)+e^8 (16+84 x^2-46 x^4+6 x^6)+e^4 (-32 x-40 x^3+28 x^5-4 x^7)+(32 x+40 x^3-28 x^5+4 x^7+e^{12} (-64+32 x^2-4 x^4)+e^8 (192 x-96 x^3+12 x^5)+e^4 (-32-168 x^2+92 x^4-12 x^6)) \log (x)+(16+84 x^2-46 x^4+6 x^6+e^8 (96-48 x^2+6 x^4)+e^4 (-192 x+96 x^3-12 x^5)) \log ^2(x)+(64 x-32 x^3+4 x^5+e^4 (-64+32 x^2-4 x^4)) \log ^3(x)+(16-8 x^2+x^4) \log ^4(x)} \, dx\)
Optimal. Leaf size=38 \[ x+\frac {x^2}{\frac {x \left (-\frac {2}{x}+x\right )}{-4+x^2}+\left (e^4-x-\log (x)\right )^2} \]
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Rubi [F] time = 29.99, 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 {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(4 + 16*x - 20*x^2 - 8*x^3 + 21*x^4 + 2*x^5 - 8*x^6 + x^8 + E^16*(16 - 8*x^2 + x^4) + E^12*(-64*x + 32*x^3
- 4*x^5) + E^8*(16 + 32*x + 84*x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6) + E^4*(-32*x^2 - 56*x^3 + 16*x^4 + 30*x
^5 - 2*x^6 - 4*x^7) + (32*x^2 + 56*x^3 - 16*x^4 - 30*x^5 + 2*x^6 + 4*x^7 + E^12*(-64 + 32*x^2 - 4*x^4) + E^8*(
192*x - 96*x^3 + 12*x^5) + E^4*(-32 - 64*x - 168*x^2 + 32*x^3 + 92*x^4 - 4*x^5 - 12*x^6))*Log[x] + (16 + 32*x
+ 84*x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6 + E^8*(96 - 48*x^2 + 6*x^4) + E^4*(-192*x + 96*x^3 - 12*x^5))*Log[x
]^2 + (64*x - 32*x^3 + 4*x^5 + E^4*(-64 + 32*x^2 - 4*x^4))*Log[x]^3 + (16 - 8*x^2 + x^4)*Log[x]^4)/(4 + 12*x^2
+ 5*x^4 - 6*x^6 + x^8 + E^16*(16 - 8*x^2 + x^4) + E^12*(-64*x + 32*x^3 - 4*x^5) + E^8*(16 + 84*x^2 - 46*x^4 +
6*x^6) + E^4*(-32*x - 40*x^3 + 28*x^5 - 4*x^7) + (32*x + 40*x^3 - 28*x^5 + 4*x^7 + E^12*(-64 + 32*x^2 - 4*x^4
) + E^8*(192*x - 96*x^3 + 12*x^5) + E^4*(-32 - 168*x^2 + 92*x^4 - 12*x^6))*Log[x] + (16 + 84*x^2 - 46*x^4 + 6*
x^6 + E^8*(96 - 48*x^2 + 6*x^4) + E^4*(-192*x + 96*x^3 - 12*x^5))*Log[x]^2 + (64*x - 32*x^3 + 4*x^5 + E^4*(-64
+ 32*x^2 - 4*x^4))*Log[x]^3 + (16 - 8*x^2 + x^4)*Log[x]^4),x]
[Out]
x + 32*E^4*Defer[Int][x/(2 + 3*x^2 - x^4 - E^8*(-4 + x^2) + 2*E^4*x*(-4 + x^2) - 2*(-E^4 + x)*(-4 + x^2)*Log[x
] - (-4 + x^2)*Log[x]^2)^2, x] - 32*(1 - E^4)*Defer[Int][x^2/(2 + 3*x^2 - x^4 - E^8*(-4 + x^2) + 2*E^4*x*(-4 +
x^2) - 2*(-E^4 + x)*(-4 + x^2)*Log[x] - (-4 + x^2)*Log[x]^2)^2, x] - 4*(7 + 4*E^4)*Defer[Int][x^3/(2 + 3*x^2
- x^4 - E^8*(-4 + x^2) + 2*E^4*x*(-4 + x^2) - 2*(-E^4 + x)*(-4 + x^2)*Log[x] - (-4 + x^2)*Log[x]^2)^2, x] + 16
*(1 - E^4)*Defer[Int][x^4/(2 + 3*x^2 - x^4 - E^8*(-4 + x^2) + 2*E^4*x*(-4 + x^2) - 2*(-E^4 + x)*(-4 + x^2)*Log
[x] - (-4 + x^2)*Log[x]^2)^2, x] + 2*(8 + E^4)*Defer[Int][x^5/(2 + 3*x^2 - x^4 - E^8*(-4 + x^2) + 2*E^4*x*(-4
+ x^2) - 2*(-E^4 + x)*(-4 + x^2)*Log[x] - (-4 + x^2)*Log[x]^2)^2, x] - 2*(1 - E^4)*Defer[Int][x^6/(2 + 3*x^2 -
x^4 - E^8*(-4 + x^2) + 2*E^4*x*(-4 + x^2) - 2*(-E^4 + x)*(-4 + x^2)*Log[x] - (-4 + x^2)*Log[x]^2)^2, x] - 2*D
efer[Int][x^7/(2 + 3*x^2 - x^4 - E^8*(-4 + x^2) + 2*E^4*x*(-4 + x^2) - 2*(-E^4 + x)*(-4 + x^2)*Log[x] - (-4 +
x^2)*Log[x]^2)^2, x] - 32*Defer[Int][(x*Log[x])/(2 + 3*x^2 - x^4 - E^8*(-4 + x^2) + 2*E^4*x*(-4 + x^2) - 2*(-E
^4 + x)*(-4 + x^2)*Log[x] - (-4 + x^2)*Log[x]^2)^2, x] - 32*Defer[Int][(x^2*Log[x])/(2 + 3*x^2 - x^4 - E^8*(-4
+ x^2) + 2*E^4*x*(-4 + x^2) - 2*(-E^4 + x)*(-4 + x^2)*Log[x] - (-4 + x^2)*Log[x]^2)^2, x] + 16*Defer[Int][(x^
3*Log[x])/(2 + 3*x^2 - x^4 - E^8*(-4 + x^2) + 2*E^4*x*(-4 + x^2) - 2*(-E^4 + x)*(-4 + x^2)*Log[x] - (-4 + x^2)
*Log[x]^2)^2, x] + 16*Defer[Int][(x^4*Log[x])/(2 + 3*x^2 - x^4 - E^8*(-4 + x^2) + 2*E^4*x*(-4 + x^2) - 2*(-E^4
+ x)*(-4 + x^2)*Log[x] - (-4 + x^2)*Log[x]^2)^2, x] - 2*Defer[Int][(x^5*Log[x])/(2 + 3*x^2 - x^4 - E^8*(-4 +
x^2) + 2*E^4*x*(-4 + x^2) - 2*(-E^4 + x)*(-4 + x^2)*Log[x] - (-4 + x^2)*Log[x]^2)^2, x] - 2*Defer[Int][(x^6*Lo
g[x])/(2 + 3*x^2 - x^4 - E^8*(-4 + x^2) + 2*E^4*x*(-4 + x^2) - 2*(-E^4 + x)*(-4 + x^2)*Log[x] - (-4 + x^2)*Log
[x]^2)^2, x] + 8*Defer[Int][x/(2 + 3*x^2 - x^4 - E^8*(-4 + x^2) + 2*E^4*x*(-4 + x^2) - 2*(-E^4 + x)*(-4 + x^2)
*Log[x] - (-4 + x^2)*Log[x]^2), x] + 2*Defer[Int][x^3/(-2 - 3*x^2 + x^4 + E^8*(-4 + x^2) - 2*E^4*x*(-4 + x^2)
+ 2*(-E^4 + x)*(-4 + x^2)*Log[x] + (-4 + x^2)*Log[x]^2), x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (-4+x^2\right )^2-4 e^{12} x \left (-4+x^2\right )^2-2 e^4 x^2 \left (16+28 x-8 x^2-15 x^3+x^4+2 x^5\right )+2 e^8 \left (8+16 x+42 x^2-8 x^3-23 x^4+x^5+3 x^6\right )-2 \left (2 e^{12} \left (-4+x^2\right )^2-6 e^8 x \left (-4+x^2\right )^2-x^2 \left (16+28 x-8 x^2-15 x^3+x^4+2 x^5\right )+2 e^4 \left (8+16 x+42 x^2-8 x^3-23 x^4+x^5+3 x^6\right )\right ) \log (x)+2 \left (8+16 x+42 x^2-8 x^3-23 x^4+x^5+3 x^6+3 e^8 \left (-4+x^2\right )^2-6 e^4 x \left (-4+x^2\right )^2\right ) \log ^2(x)-4 \left (e^4-x\right ) \left (-4+x^2\right )^2 \log ^3(x)+\left (-4+x^2\right )^2 \log ^4(x)}{\left (2+3 x^2-x^4-e^8 \left (-4+x^2\right )+2 e^4 x \left (-4+x^2\right )-2 \left (-e^4+x\right ) \left (-4+x^2\right ) \log (x)-\left (-4+x^2\right ) \log ^2(x)\right )^2} \, dx\\ &=\int \left (1+\frac {2 x \left (16 e^4-16 \left (1-e^4\right ) x-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 \left (1-e^4\right ) x^3+8 \left (1+\frac {e^4}{8}\right ) x^4-\left (1-e^4\right ) x^5-x^6-16 \log (x)-16 x \log (x)+8 x^2 \log (x)+8 x^3 \log (x)-x^4 \log (x)-x^5 \log (x)\right )}{\left (2 \left (1+2 e^8\right )-8 e^4 x+3 \left (1-\frac {e^8}{3}\right ) x^2+2 e^4 x^3-x^4-8 e^4 \log (x)+8 x \log (x)+2 e^4 x^2 \log (x)-2 x^3 \log (x)+4 \log ^2(x)-x^2 \log ^2(x)\right )^2}+\frac {2 x \left (4-x^2\right )}{2 \left (1+2 e^8\right )-8 e^4 x+3 \left (1-\frac {e^8}{3}\right ) x^2+2 e^4 x^3-x^4-8 e^4 \log (x)+8 x \log (x)+2 e^4 x^2 \log (x)-2 x^3 \log (x)+4 \log ^2(x)-x^2 \log ^2(x)}\right ) \, dx\\ &=x+2 \int \frac {x \left (16 e^4-16 \left (1-e^4\right ) x-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 \left (1-e^4\right ) x^3+8 \left (1+\frac {e^4}{8}\right ) x^4-\left (1-e^4\right ) x^5-x^6-16 \log (x)-16 x \log (x)+8 x^2 \log (x)+8 x^3 \log (x)-x^4 \log (x)-x^5 \log (x)\right )}{\left (2 \left (1+2 e^8\right )-8 e^4 x+3 \left (1-\frac {e^8}{3}\right ) x^2+2 e^4 x^3-x^4-8 e^4 \log (x)+8 x \log (x)+2 e^4 x^2 \log (x)-2 x^3 \log (x)+4 \log ^2(x)-x^2 \log ^2(x)\right )^2} \, dx+2 \int \frac {x \left (4-x^2\right )}{2 \left (1+2 e^8\right )-8 e^4 x+3 \left (1-\frac {e^8}{3}\right ) x^2+2 e^4 x^3-x^4-8 e^4 \log (x)+8 x \log (x)+2 e^4 x^2 \log (x)-2 x^3 \log (x)+4 \log ^2(x)-x^2 \log ^2(x)} \, dx\\ &=x+2 \int \frac {x \left (e^4 (1+x) \left (-4+x^2\right )^2-x \left (16+14 x-8 x^2-8 x^3+x^4+x^5\right )-(1+x) \left (-4+x^2\right )^2 \log (x)\right )}{\left (2+3 x^2-x^4-e^8 \left (-4+x^2\right )+2 e^4 x \left (-4+x^2\right )-2 \left (-e^4+x\right ) \left (-4+x^2\right ) \log (x)-\left (-4+x^2\right ) \log ^2(x)\right )^2} \, dx+2 \int \frac {x \left (4-x^2\right )}{2+3 x^2-x^4-e^8 \left (-4+x^2\right )+2 e^4 x \left (-4+x^2\right )-2 \left (-e^4+x\right ) \left (-4+x^2\right ) \log (x)-\left (-4+x^2\right ) \log ^2(x)} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.29, size = 69, normalized size = 1.82 \begin {gather*} x+\frac {x^2 \left (-4+x^2\right )}{-2-3 x^2+x^4+e^8 \left (-4+x^2\right )-2 e^4 x \left (-4+x^2\right )+2 \left (-e^4+x\right ) \left (-4+x^2\right ) \log (x)+\left (-4+x^2\right ) \log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(4 + 16*x - 20*x^2 - 8*x^3 + 21*x^4 + 2*x^5 - 8*x^6 + x^8 + E^16*(16 - 8*x^2 + x^4) + E^12*(-64*x +
32*x^3 - 4*x^5) + E^8*(16 + 32*x + 84*x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6) + E^4*(-32*x^2 - 56*x^3 + 16*x^4
+ 30*x^5 - 2*x^6 - 4*x^7) + (32*x^2 + 56*x^3 - 16*x^4 - 30*x^5 + 2*x^6 + 4*x^7 + E^12*(-64 + 32*x^2 - 4*x^4) +
E^8*(192*x - 96*x^3 + 12*x^5) + E^4*(-32 - 64*x - 168*x^2 + 32*x^3 + 92*x^4 - 4*x^5 - 12*x^6))*Log[x] + (16 +
32*x + 84*x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6 + E^8*(96 - 48*x^2 + 6*x^4) + E^4*(-192*x + 96*x^3 - 12*x^5))
*Log[x]^2 + (64*x - 32*x^3 + 4*x^5 + E^4*(-64 + 32*x^2 - 4*x^4))*Log[x]^3 + (16 - 8*x^2 + x^4)*Log[x]^4)/(4 +
12*x^2 + 5*x^4 - 6*x^6 + x^8 + E^16*(16 - 8*x^2 + x^4) + E^12*(-64*x + 32*x^3 - 4*x^5) + E^8*(16 + 84*x^2 - 46
*x^4 + 6*x^6) + E^4*(-32*x - 40*x^3 + 28*x^5 - 4*x^7) + (32*x + 40*x^3 - 28*x^5 + 4*x^7 + E^12*(-64 + 32*x^2 -
4*x^4) + E^8*(192*x - 96*x^3 + 12*x^5) + E^4*(-32 - 168*x^2 + 92*x^4 - 12*x^6))*Log[x] + (16 + 84*x^2 - 46*x^
4 + 6*x^6 + E^8*(96 - 48*x^2 + 6*x^4) + E^4*(-192*x + 96*x^3 - 12*x^5))*Log[x]^2 + (64*x - 32*x^3 + 4*x^5 + E^
4*(-64 + 32*x^2 - 4*x^4))*Log[x]^3 + (16 - 8*x^2 + x^4)*Log[x]^4),x]
[Out]
x + (x^2*(-4 + x^2))/(-2 - 3*x^2 + x^4 + E^8*(-4 + x^2) - 2*E^4*x*(-4 + x^2) + 2*(-E^4 + x)*(-4 + x^2)*Log[x]
+ (-4 + x^2)*Log[x]^2)
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fricas [B] time = 0.58, size = 141, normalized size = 3.71 \begin {gather*} \frac {x^{5} + x^{4} - 3 \, x^{3} + {\left (x^{3} - 4 \, x\right )} \log \relax (x)^{2} - 4 \, x^{2} + {\left (x^{3} - 4 \, x\right )} e^{8} - 2 \, {\left (x^{4} - 4 \, x^{2}\right )} e^{4} + 2 \, {\left (x^{4} - 4 \, x^{2} - {\left (x^{3} - 4 \, x\right )} e^{4}\right )} \log \relax (x) - 2 \, x}{x^{4} + {\left (x^{2} - 4\right )} \log \relax (x)^{2} - 3 \, x^{2} + {\left (x^{2} - 4\right )} e^{8} - 2 \, {\left (x^{3} - 4 \, x\right )} e^{4} + 2 \, {\left (x^{3} - {\left (x^{2} - 4\right )} e^{4} - 4 \, x\right )} \log \relax (x) - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x^4-8*x^2+16)*log(x)^4+((-4*x^4+32*x^2-64)*exp(4)+4*x^5-32*x^3+64*x)*log(x)^3+((6*x^4-48*x^2+96)*e
xp(4)^2+(-12*x^5+96*x^3-192*x)*exp(4)+6*x^6+2*x^5-46*x^4-16*x^3+84*x^2+32*x+16)*log(x)^2+((-4*x^4+32*x^2-64)*e
xp(4)^3+(12*x^5-96*x^3+192*x)*exp(4)^2+(-12*x^6-4*x^5+92*x^4+32*x^3-168*x^2-64*x-32)*exp(4)+4*x^7+2*x^6-30*x^5
-16*x^4+56*x^3+32*x^2)*log(x)+(x^4-8*x^2+16)*exp(4)^4+(-4*x^5+32*x^3-64*x)*exp(4)^3+(6*x^6+2*x^5-46*x^4-16*x^3
+84*x^2+32*x+16)*exp(4)^2+(-4*x^7-2*x^6+30*x^5+16*x^4-56*x^3-32*x^2)*exp(4)+x^8-8*x^6+2*x^5+21*x^4-8*x^3-20*x^
2+16*x+4)/((x^4-8*x^2+16)*log(x)^4+((-4*x^4+32*x^2-64)*exp(4)+4*x^5-32*x^3+64*x)*log(x)^3+((6*x^4-48*x^2+96)*e
xp(4)^2+(-12*x^5+96*x^3-192*x)*exp(4)+6*x^6-46*x^4+84*x^2+16)*log(x)^2+((-4*x^4+32*x^2-64)*exp(4)^3+(12*x^5-96
*x^3+192*x)*exp(4)^2+(-12*x^6+92*x^4-168*x^2-32)*exp(4)+4*x^7-28*x^5+40*x^3+32*x)*log(x)+(x^4-8*x^2+16)*exp(4)
^4+(-4*x^5+32*x^3-64*x)*exp(4)^3+(6*x^6-46*x^4+84*x^2+16)*exp(4)^2+(-4*x^7+28*x^5-40*x^3-32*x)*exp(4)+x^8-6*x^
6+5*x^4+12*x^2+4),x, algorithm="fricas")
[Out]
(x^5 + x^4 - 3*x^3 + (x^3 - 4*x)*log(x)^2 - 4*x^2 + (x^3 - 4*x)*e^8 - 2*(x^4 - 4*x^2)*e^4 + 2*(x^4 - 4*x^2 - (
x^3 - 4*x)*e^4)*log(x) - 2*x)/(x^4 + (x^2 - 4)*log(x)^2 - 3*x^2 + (x^2 - 4)*e^8 - 2*(x^3 - 4*x)*e^4 + 2*(x^3 -
(x^2 - 4)*e^4 - 4*x)*log(x) - 2)
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giac [B] time = 38.05, size = 168, normalized size = 4.42 \begin {gather*} \frac {x^{5} - 2 \, x^{4} e^{4} + 2 \, x^{4} \log \relax (x) - 2 \, x^{3} e^{4} \log \relax (x) + x^{3} \log \relax (x)^{2} + 2 \, x^{4} + x^{3} e^{8} - 3 \, x^{3} + 8 \, x^{2} e^{4} - 8 \, x^{2} \log \relax (x) + 8 \, x e^{4} \log \relax (x) - 4 \, x \log \relax (x)^{2} - 8 \, x^{2} - 4 \, x e^{8} - 2 \, x}{x^{4} - 2 \, x^{3} e^{4} + 2 \, x^{3} \log \relax (x) - 2 \, x^{2} e^{4} \log \relax (x) + x^{2} \log \relax (x)^{2} + x^{2} e^{8} - 3 \, x^{2} + 8 \, x e^{4} - 8 \, x \log \relax (x) + 8 \, e^{4} \log \relax (x) - 4 \, \log \relax (x)^{2} - 4 \, e^{8} - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x^4-8*x^2+16)*log(x)^4+((-4*x^4+32*x^2-64)*exp(4)+4*x^5-32*x^3+64*x)*log(x)^3+((6*x^4-48*x^2+96)*e
xp(4)^2+(-12*x^5+96*x^3-192*x)*exp(4)+6*x^6+2*x^5-46*x^4-16*x^3+84*x^2+32*x+16)*log(x)^2+((-4*x^4+32*x^2-64)*e
xp(4)^3+(12*x^5-96*x^3+192*x)*exp(4)^2+(-12*x^6-4*x^5+92*x^4+32*x^3-168*x^2-64*x-32)*exp(4)+4*x^7+2*x^6-30*x^5
-16*x^4+56*x^3+32*x^2)*log(x)+(x^4-8*x^2+16)*exp(4)^4+(-4*x^5+32*x^3-64*x)*exp(4)^3+(6*x^6+2*x^5-46*x^4-16*x^3
+84*x^2+32*x+16)*exp(4)^2+(-4*x^7-2*x^6+30*x^5+16*x^4-56*x^3-32*x^2)*exp(4)+x^8-8*x^6+2*x^5+21*x^4-8*x^3-20*x^
2+16*x+4)/((x^4-8*x^2+16)*log(x)^4+((-4*x^4+32*x^2-64)*exp(4)+4*x^5-32*x^3+64*x)*log(x)^3+((6*x^4-48*x^2+96)*e
xp(4)^2+(-12*x^5+96*x^3-192*x)*exp(4)+6*x^6-46*x^4+84*x^2+16)*log(x)^2+((-4*x^4+32*x^2-64)*exp(4)^3+(12*x^5-96
*x^3+192*x)*exp(4)^2+(-12*x^6+92*x^4-168*x^2-32)*exp(4)+4*x^7-28*x^5+40*x^3+32*x)*log(x)+(x^4-8*x^2+16)*exp(4)
^4+(-4*x^5+32*x^3-64*x)*exp(4)^3+(6*x^6-46*x^4+84*x^2+16)*exp(4)^2+(-4*x^7+28*x^5-40*x^3-32*x)*exp(4)+x^8-6*x^
6+5*x^4+12*x^2+4),x, algorithm="giac")
[Out]
(x^5 - 2*x^4*e^4 + 2*x^4*log(x) - 2*x^3*e^4*log(x) + x^3*log(x)^2 + 2*x^4 + x^3*e^8 - 3*x^3 + 8*x^2*e^4 - 8*x^
2*log(x) + 8*x*e^4*log(x) - 4*x*log(x)^2 - 8*x^2 - 4*x*e^8 - 2*x)/(x^4 - 2*x^3*e^4 + 2*x^3*log(x) - 2*x^2*e^4*
log(x) + x^2*log(x)^2 + x^2*e^8 - 3*x^2 + 8*x*e^4 - 8*x*log(x) + 8*e^4*log(x) - 4*log(x)^2 - 4*e^8 - 2)
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maple [B] time = 0.13, size = 87, normalized size = 2.29
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\(x +\frac {x^{2} \left (x^{2}-4\right )}{x^{2} \ln \relax (x )^{2}-2 x^{2} {\mathrm e}^{4} \ln \relax (x )+2 x^{3} \ln \relax (x )+x^{2} {\mathrm e}^{8}-2 x^{3} {\mathrm e}^{4}+x^{4}-4 \ln \relax (x )^{2}+8 \,{\mathrm e}^{4} \ln \relax (x )-8 x \ln \relax (x )-4 \,{\mathrm e}^{8}+8 x \,{\mathrm e}^{4}-3 x^{2}-2}\) |
\(87\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((x^4-8*x^2+16)*ln(x)^4+((-4*x^4+32*x^2-64)*exp(4)+4*x^5-32*x^3+64*x)*ln(x)^3+((6*x^4-48*x^2+96)*exp(4)^2+
(-12*x^5+96*x^3-192*x)*exp(4)+6*x^6+2*x^5-46*x^4-16*x^3+84*x^2+32*x+16)*ln(x)^2+((-4*x^4+32*x^2-64)*exp(4)^3+(
12*x^5-96*x^3+192*x)*exp(4)^2+(-12*x^6-4*x^5+92*x^4+32*x^3-168*x^2-64*x-32)*exp(4)+4*x^7+2*x^6-30*x^5-16*x^4+5
6*x^3+32*x^2)*ln(x)+(x^4-8*x^2+16)*exp(4)^4+(-4*x^5+32*x^3-64*x)*exp(4)^3+(6*x^6+2*x^5-46*x^4-16*x^3+84*x^2+32
*x+16)*exp(4)^2+(-4*x^7-2*x^6+30*x^5+16*x^4-56*x^3-32*x^2)*exp(4)+x^8-8*x^6+2*x^5+21*x^4-8*x^3-20*x^2+16*x+4)/
((x^4-8*x^2+16)*ln(x)^4+((-4*x^4+32*x^2-64)*exp(4)+4*x^5-32*x^3+64*x)*ln(x)^3+((6*x^4-48*x^2+96)*exp(4)^2+(-12
*x^5+96*x^3-192*x)*exp(4)+6*x^6-46*x^4+84*x^2+16)*ln(x)^2+((-4*x^4+32*x^2-64)*exp(4)^3+(12*x^5-96*x^3+192*x)*e
xp(4)^2+(-12*x^6+92*x^4-168*x^2-32)*exp(4)+4*x^7-28*x^5+40*x^3+32*x)*ln(x)+(x^4-8*x^2+16)*exp(4)^4+(-4*x^5+32*
x^3-64*x)*exp(4)^3+(6*x^6-46*x^4+84*x^2+16)*exp(4)^2+(-4*x^7+28*x^5-40*x^3-32*x)*exp(4)+x^8-6*x^6+5*x^4+12*x^2
+4),x,method=_RETURNVERBOSE)
[Out]
x+x^2*(x^2-4)/(x^2*ln(x)^2-2*x^2*exp(4)*ln(x)+2*x^3*ln(x)+x^2*exp(8)-2*x^3*exp(4)+x^4-4*ln(x)^2+8*exp(4)*ln(x)
-8*x*ln(x)-4*exp(8)+8*x*exp(4)-3*x^2-2)
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maxima [B] time = 0.90, size = 144, normalized size = 3.79 \begin {gather*} \frac {x^{5} - x^{4} {\left (2 \, e^{4} - 1\right )} + x^{3} {\left (e^{8} - 3\right )} + 4 \, x^{2} {\left (2 \, e^{4} - 1\right )} + {\left (x^{3} - 4 \, x\right )} \log \relax (x)^{2} - 2 \, x {\left (2 \, e^{8} + 1\right )} + 2 \, {\left (x^{4} - x^{3} e^{4} - 4 \, x^{2} + 4 \, x e^{4}\right )} \log \relax (x)}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 3\right )} + {\left (x^{2} - 4\right )} \log \relax (x)^{2} + 8 \, x e^{4} + 2 \, {\left (x^{3} - x^{2} e^{4} - 4 \, x + 4 \, e^{4}\right )} \log \relax (x) - 4 \, e^{8} - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x^4-8*x^2+16)*log(x)^4+((-4*x^4+32*x^2-64)*exp(4)+4*x^5-32*x^3+64*x)*log(x)^3+((6*x^4-48*x^2+96)*e
xp(4)^2+(-12*x^5+96*x^3-192*x)*exp(4)+6*x^6+2*x^5-46*x^4-16*x^3+84*x^2+32*x+16)*log(x)^2+((-4*x^4+32*x^2-64)*e
xp(4)^3+(12*x^5-96*x^3+192*x)*exp(4)^2+(-12*x^6-4*x^5+92*x^4+32*x^3-168*x^2-64*x-32)*exp(4)+4*x^7+2*x^6-30*x^5
-16*x^4+56*x^3+32*x^2)*log(x)+(x^4-8*x^2+16)*exp(4)^4+(-4*x^5+32*x^3-64*x)*exp(4)^3+(6*x^6+2*x^5-46*x^4-16*x^3
+84*x^2+32*x+16)*exp(4)^2+(-4*x^7-2*x^6+30*x^5+16*x^4-56*x^3-32*x^2)*exp(4)+x^8-8*x^6+2*x^5+21*x^4-8*x^3-20*x^
2+16*x+4)/((x^4-8*x^2+16)*log(x)^4+((-4*x^4+32*x^2-64)*exp(4)+4*x^5-32*x^3+64*x)*log(x)^3+((6*x^4-48*x^2+96)*e
xp(4)^2+(-12*x^5+96*x^3-192*x)*exp(4)+6*x^6-46*x^4+84*x^2+16)*log(x)^2+((-4*x^4+32*x^2-64)*exp(4)^3+(12*x^5-96
*x^3+192*x)*exp(4)^2+(-12*x^6+92*x^4-168*x^2-32)*exp(4)+4*x^7-28*x^5+40*x^3+32*x)*log(x)+(x^4-8*x^2+16)*exp(4)
^4+(-4*x^5+32*x^3-64*x)*exp(4)^3+(6*x^6-46*x^4+84*x^2+16)*exp(4)^2+(-4*x^7+28*x^5-40*x^3-32*x)*exp(4)+x^8-6*x^
6+5*x^4+12*x^2+4),x, algorithm="maxima")
[Out]
(x^5 - x^4*(2*e^4 - 1) + x^3*(e^8 - 3) + 4*x^2*(2*e^4 - 1) + (x^3 - 4*x)*log(x)^2 - 2*x*(2*e^8 + 1) + 2*(x^4 -
x^3*e^4 - 4*x^2 + 4*x*e^4)*log(x))/(x^4 - 2*x^3*e^4 + x^2*(e^8 - 3) + (x^2 - 4)*log(x)^2 + 8*x*e^4 + 2*(x^3 -
x^2*e^4 - 4*x + 4*e^4)*log(x) - 4*e^8 - 2)
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {16\,x+{\mathrm {e}}^8\,\left (6\,x^6+2\,x^5-46\,x^4-16\,x^3+84\,x^2+32\,x+16\right )+{\ln \relax (x)}^4\,\left (x^4-8\,x^2+16\right )+{\mathrm {e}}^{16}\,\left (x^4-8\,x^2+16\right )-{\mathrm {e}}^{12}\,\left (4\,x^5-32\,x^3+64\,x\right )-{\mathrm {e}}^4\,\left (4\,x^7+2\,x^6-30\,x^5-16\,x^4+56\,x^3+32\,x^2\right )-20\,x^2-8\,x^3+21\,x^4+2\,x^5-8\,x^6+x^8+{\ln \relax (x)}^3\,\left (64\,x-{\mathrm {e}}^4\,\left (4\,x^4-32\,x^2+64\right )-32\,x^3+4\,x^5\right )+{\ln \relax (x)}^2\,\left (32\,x-{\mathrm {e}}^4\,\left (12\,x^5-96\,x^3+192\,x\right )+{\mathrm {e}}^8\,\left (6\,x^4-48\,x^2+96\right )+84\,x^2-16\,x^3-46\,x^4+2\,x^5+6\,x^6+16\right )+\ln \relax (x)\,\left ({\mathrm {e}}^8\,\left (12\,x^5-96\,x^3+192\,x\right )-{\mathrm {e}}^4\,\left (12\,x^6+4\,x^5-92\,x^4-32\,x^3+168\,x^2+64\,x+32\right )-{\mathrm {e}}^{12}\,\left (4\,x^4-32\,x^2+64\right )+32\,x^2+56\,x^3-16\,x^4-30\,x^5+2\,x^6+4\,x^7\right )+4}{{\ln \relax (x)}^4\,\left (x^4-8\,x^2+16\right )+{\mathrm {e}}^{16}\,\left (x^4-8\,x^2+16\right )-{\mathrm {e}}^{12}\,\left (4\,x^5-32\,x^3+64\,x\right )-{\mathrm {e}}^4\,\left (4\,x^7-28\,x^5+40\,x^3+32\,x\right )+{\ln \relax (x)}^2\,\left ({\mathrm {e}}^8\,\left (6\,x^4-48\,x^2+96\right )-{\mathrm {e}}^4\,\left (12\,x^5-96\,x^3+192\,x\right )+84\,x^2-46\,x^4+6\,x^6+16\right )+{\mathrm {e}}^8\,\left (6\,x^6-46\,x^4+84\,x^2+16\right )+12\,x^2+5\,x^4-6\,x^6+x^8+{\ln \relax (x)}^3\,\left (64\,x-{\mathrm {e}}^4\,\left (4\,x^4-32\,x^2+64\right )-32\,x^3+4\,x^5\right )+\ln \relax (x)\,\left (32\,x+{\mathrm {e}}^8\,\left (12\,x^5-96\,x^3+192\,x\right )-{\mathrm {e}}^{12}\,\left (4\,x^4-32\,x^2+64\right )-{\mathrm {e}}^4\,\left (12\,x^6-92\,x^4+168\,x^2+32\right )+40\,x^3-28\,x^5+4\,x^7\right )+4} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((16*x + exp(8)*(32*x + 84*x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6 + 16) + log(x)^4*(x^4 - 8*x^2 + 16) + exp(
16)*(x^4 - 8*x^2 + 16) - exp(12)*(64*x - 32*x^3 + 4*x^5) - exp(4)*(32*x^2 + 56*x^3 - 16*x^4 - 30*x^5 + 2*x^6 +
4*x^7) - 20*x^2 - 8*x^3 + 21*x^4 + 2*x^5 - 8*x^6 + x^8 + log(x)^3*(64*x - exp(4)*(4*x^4 - 32*x^2 + 64) - 32*x
^3 + 4*x^5) + log(x)^2*(32*x - exp(4)*(192*x - 96*x^3 + 12*x^5) + exp(8)*(6*x^4 - 48*x^2 + 96) + 84*x^2 - 16*x
^3 - 46*x^4 + 2*x^5 + 6*x^6 + 16) + log(x)*(exp(8)*(192*x - 96*x^3 + 12*x^5) - exp(4)*(64*x + 168*x^2 - 32*x^3
- 92*x^4 + 4*x^5 + 12*x^6 + 32) - exp(12)*(4*x^4 - 32*x^2 + 64) + 32*x^2 + 56*x^3 - 16*x^4 - 30*x^5 + 2*x^6 +
4*x^7) + 4)/(log(x)^4*(x^4 - 8*x^2 + 16) + exp(16)*(x^4 - 8*x^2 + 16) - exp(12)*(64*x - 32*x^3 + 4*x^5) - exp
(4)*(32*x + 40*x^3 - 28*x^5 + 4*x^7) + log(x)^2*(exp(8)*(6*x^4 - 48*x^2 + 96) - exp(4)*(192*x - 96*x^3 + 12*x^
5) + 84*x^2 - 46*x^4 + 6*x^6 + 16) + exp(8)*(84*x^2 - 46*x^4 + 6*x^6 + 16) + 12*x^2 + 5*x^4 - 6*x^6 + x^8 + lo
g(x)^3*(64*x - exp(4)*(4*x^4 - 32*x^2 + 64) - 32*x^3 + 4*x^5) + log(x)*(32*x + exp(8)*(192*x - 96*x^3 + 12*x^5
) - exp(12)*(4*x^4 - 32*x^2 + 64) - exp(4)*(168*x^2 - 92*x^4 + 12*x^6 + 32) + 40*x^3 - 28*x^5 + 4*x^7) + 4),x)
[Out]
int((16*x + exp(8)*(32*x + 84*x^2 - 16*x^3 - 46*x^4 + 2*x^5 + 6*x^6 + 16) + log(x)^4*(x^4 - 8*x^2 + 16) + exp(
16)*(x^4 - 8*x^2 + 16) - exp(12)*(64*x - 32*x^3 + 4*x^5) - exp(4)*(32*x^2 + 56*x^3 - 16*x^4 - 30*x^5 + 2*x^6 +
4*x^7) - 20*x^2 - 8*x^3 + 21*x^4 + 2*x^5 - 8*x^6 + x^8 + log(x)^3*(64*x - exp(4)*(4*x^4 - 32*x^2 + 64) - 32*x
^3 + 4*x^5) + log(x)^2*(32*x - exp(4)*(192*x - 96*x^3 + 12*x^5) + exp(8)*(6*x^4 - 48*x^2 + 96) + 84*x^2 - 16*x
^3 - 46*x^4 + 2*x^5 + 6*x^6 + 16) + log(x)*(exp(8)*(192*x - 96*x^3 + 12*x^5) - exp(4)*(64*x + 168*x^2 - 32*x^3
- 92*x^4 + 4*x^5 + 12*x^6 + 32) - exp(12)*(4*x^4 - 32*x^2 + 64) + 32*x^2 + 56*x^3 - 16*x^4 - 30*x^5 + 2*x^6 +
4*x^7) + 4)/(log(x)^4*(x^4 - 8*x^2 + 16) + exp(16)*(x^4 - 8*x^2 + 16) - exp(12)*(64*x - 32*x^3 + 4*x^5) - exp
(4)*(32*x + 40*x^3 - 28*x^5 + 4*x^7) + log(x)^2*(exp(8)*(6*x^4 - 48*x^2 + 96) - exp(4)*(192*x - 96*x^3 + 12*x^
5) + 84*x^2 - 46*x^4 + 6*x^6 + 16) + exp(8)*(84*x^2 - 46*x^4 + 6*x^6 + 16) + 12*x^2 + 5*x^4 - 6*x^6 + x^8 + lo
g(x)^3*(64*x - exp(4)*(4*x^4 - 32*x^2 + 64) - 32*x^3 + 4*x^5) + log(x)*(32*x + exp(8)*(192*x - 96*x^3 + 12*x^5
) - exp(12)*(4*x^4 - 32*x^2 + 64) - exp(4)*(168*x^2 - 92*x^4 + 12*x^6 + 32) + 40*x^3 - 28*x^5 + 4*x^7) + 4), x
)
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sympy [B] time = 1.02, size = 82, normalized size = 2.16 \begin {gather*} x + \frac {x^{4} - 4 x^{2}}{x^{4} - 2 x^{3} e^{4} - 3 x^{2} + x^{2} e^{8} + 8 x e^{4} + \left (x^{2} - 4\right ) \log {\relax (x )}^{2} + \left (2 x^{3} - 2 x^{2} e^{4} - 8 x + 8 e^{4}\right ) \log {\relax (x )} - 4 e^{8} - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((x**4-8*x**2+16)*ln(x)**4+((-4*x**4+32*x**2-64)*exp(4)+4*x**5-32*x**3+64*x)*ln(x)**3+((6*x**4-48*x*
*2+96)*exp(4)**2+(-12*x**5+96*x**3-192*x)*exp(4)+6*x**6+2*x**5-46*x**4-16*x**3+84*x**2+32*x+16)*ln(x)**2+((-4*
x**4+32*x**2-64)*exp(4)**3+(12*x**5-96*x**3+192*x)*exp(4)**2+(-12*x**6-4*x**5+92*x**4+32*x**3-168*x**2-64*x-32
)*exp(4)+4*x**7+2*x**6-30*x**5-16*x**4+56*x**3+32*x**2)*ln(x)+(x**4-8*x**2+16)*exp(4)**4+(-4*x**5+32*x**3-64*x
)*exp(4)**3+(6*x**6+2*x**5-46*x**4-16*x**3+84*x**2+32*x+16)*exp(4)**2+(-4*x**7-2*x**6+30*x**5+16*x**4-56*x**3-
32*x**2)*exp(4)+x**8-8*x**6+2*x**5+21*x**4-8*x**3-20*x**2+16*x+4)/((x**4-8*x**2+16)*ln(x)**4+((-4*x**4+32*x**2
-64)*exp(4)+4*x**5-32*x**3+64*x)*ln(x)**3+((6*x**4-48*x**2+96)*exp(4)**2+(-12*x**5+96*x**3-192*x)*exp(4)+6*x**
6-46*x**4+84*x**2+16)*ln(x)**2+((-4*x**4+32*x**2-64)*exp(4)**3+(12*x**5-96*x**3+192*x)*exp(4)**2+(-12*x**6+92*
x**4-168*x**2-32)*exp(4)+4*x**7-28*x**5+40*x**3+32*x)*ln(x)+(x**4-8*x**2+16)*exp(4)**4+(-4*x**5+32*x**3-64*x)*
exp(4)**3+(6*x**6-46*x**4+84*x**2+16)*exp(4)**2+(-4*x**7+28*x**5-40*x**3-32*x)*exp(4)+x**8-6*x**6+5*x**4+12*x*
*2+4),x)
[Out]
x + (x**4 - 4*x**2)/(x**4 - 2*x**3*exp(4) - 3*x**2 + x**2*exp(8) + 8*x*exp(4) + (x**2 - 4)*log(x)**2 + (2*x**3
- 2*x**2*exp(4) - 8*x + 8*exp(4))*log(x) - 4*exp(8) - 2)
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