3.89.84 \(\int \frac {-128 x^2+160 x^3-32 x^4+e^5 (-640 x+128 x^2)+(-640 x+128 x^2) \log (-5+x)}{-320 x^3-176 x^4-12 x^5+7 x^6+x^7+e^{15} (-320+64 x)+e^{10} (-960 x-48 x^2+48 x^3)+e^5 (-960 x^2-288 x^3+36 x^4+12 x^5)+(-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} (-240 x+48 x^2)+e^5 (-480 x^2-24 x^3+24 x^4)) \log (2)+(-60 x^3-3 x^4+3 x^5+e^5 (-60 x^2+12 x^3)) \log ^2(2)+(-5 x^3+x^4) \log ^3(2)+(-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} (-240 x+48 x^2)+e^5 (-480 x^2-24 x^3+24 x^4)+(-120 x^3-6 x^4+6 x^5+e^5 (-120 x^2+24 x^3)) \log (2)+(-15 x^3+3 x^4) \log ^2(2)) \log (3)+(-60 x^3-3 x^4+3 x^5+e^5 (-60 x^2+12 x^3)+(-15 x^3+3 x^4) \log (2)) \log ^2(3)+(-5 x^3+x^4) \log ^3(3)+(-960 x^2-288 x^3+36 x^4+12 x^5+e^{10} (-960+192 x)+e^5 (-1920 x-96 x^2+96 x^3)+(-480 x^2-24 x^3+24 x^4+e^5 (-480 x+96 x^2)) \log (2)+(-60 x^2+12 x^3) \log ^2(2)+(-480 x^2-24 x^3+24 x^4+e^5 (-480 x+96 x^2)+(-120 x^2+24 x^3) \log (2)) \log (3)+(-60 x^2+12 x^3) \log ^2(3)) \log (-5+x)+(-960 x-48 x^2+48 x^3+e^5 (-960+192 x)+(-240 x+48 x^2) \log (2)+(-240 x+48 x^2) \log (3)) \log ^2(-5+x)+(-320+64 x) \log ^3(-5+x)} \, dx\)
Optimal. Leaf size=26 \[ \frac {1}{\left (\frac {1}{4} (x+\log (2)+\log (3))+\frac {e^5+x+\log (-5+x)}{x}\right )^2} \]
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Rubi [F] time = 3.85, 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 {-128 x^2+160 x^3-32 x^4+e^5 \left (-640 x+128 x^2\right )+\left (-640 x+128 x^2\right ) \log (-5+x)}{-320 x^3-176 x^4-12 x^5+7 x^6+x^7+e^{15} (-320+64 x)+e^{10} \left (-960 x-48 x^2+48 x^3\right )+e^5 \left (-960 x^2-288 x^3+36 x^4+12 x^5\right )+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )\right ) \log (2)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )\right ) \log ^2(2)+\left (-5 x^3+x^4\right ) \log ^3(2)+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )+\left (-120 x^3-6 x^4+6 x^5+e^5 \left (-120 x^2+24 x^3\right )\right ) \log (2)+\left (-15 x^3+3 x^4\right ) \log ^2(2)\right ) \log (3)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )+\left (-15 x^3+3 x^4\right ) \log (2)\right ) \log ^2(3)+\left (-5 x^3+x^4\right ) \log ^3(3)+\left (-960 x^2-288 x^3+36 x^4+12 x^5+e^{10} (-960+192 x)+e^5 \left (-1920 x-96 x^2+96 x^3\right )+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )\right ) \log (2)+\left (-60 x^2+12 x^3\right ) \log ^2(2)+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )+\left (-120 x^2+24 x^3\right ) \log (2)\right ) \log (3)+\left (-60 x^2+12 x^3\right ) \log ^2(3)\right ) \log (-5+x)+\left (-960 x-48 x^2+48 x^3+e^5 (-960+192 x)+\left (-240 x+48 x^2\right ) \log (2)+\left (-240 x+48 x^2\right ) \log (3)\right ) \log ^2(-5+x)+(-320+64 x) \log ^3(-5+x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(-128*x^2 + 160*x^3 - 32*x^4 + E^5*(-640*x + 128*x^2) + (-640*x + 128*x^2)*Log[-5 + x])/(-320*x^3 - 176*x^
4 - 12*x^5 + 7*x^6 + x^7 + E^15*(-320 + 64*x) + E^10*(-960*x - 48*x^2 + 48*x^3) + E^5*(-960*x^2 - 288*x^3 + 36
*x^4 + 12*x^5) + (-240*x^3 - 72*x^4 + 9*x^5 + 3*x^6 + E^10*(-240*x + 48*x^2) + E^5*(-480*x^2 - 24*x^3 + 24*x^4
))*Log[2] + (-60*x^3 - 3*x^4 + 3*x^5 + E^5*(-60*x^2 + 12*x^3))*Log[2]^2 + (-5*x^3 + x^4)*Log[2]^3 + (-240*x^3
- 72*x^4 + 9*x^5 + 3*x^6 + E^10*(-240*x + 48*x^2) + E^5*(-480*x^2 - 24*x^3 + 24*x^4) + (-120*x^3 - 6*x^4 + 6*x
^5 + E^5*(-120*x^2 + 24*x^3))*Log[2] + (-15*x^3 + 3*x^4)*Log[2]^2)*Log[3] + (-60*x^3 - 3*x^4 + 3*x^5 + E^5*(-6
0*x^2 + 12*x^3) + (-15*x^3 + 3*x^4)*Log[2])*Log[3]^2 + (-5*x^3 + x^4)*Log[3]^3 + (-960*x^2 - 288*x^3 + 36*x^4
+ 12*x^5 + E^10*(-960 + 192*x) + E^5*(-1920*x - 96*x^2 + 96*x^3) + (-480*x^2 - 24*x^3 + 24*x^4 + E^5*(-480*x +
96*x^2))*Log[2] + (-60*x^2 + 12*x^3)*Log[2]^2 + (-480*x^2 - 24*x^3 + 24*x^4 + E^5*(-480*x + 96*x^2) + (-120*x
^2 + 24*x^3)*Log[2])*Log[3] + (-60*x^2 + 12*x^3)*Log[3]^2)*Log[-5 + x] + (-960*x - 48*x^2 + 48*x^3 + E^5*(-960
+ 192*x) + (-240*x + 48*x^2)*Log[2] + (-240*x + 48*x^2)*Log[3])*Log[-5 + x]^2 + (-320 + 64*x)*Log[-5 + x]^3),
x]
[Out]
640*Defer[Int][(-4*E^5 - x*(4 + x + Log[6]) - 4*Log[-5 + x])^(-3), x] + 128*Defer[Int][x/(-4*E^5 - x*(4 + x +
Log[6]) - 4*Log[-5 + x])^3, x] + 64*Defer[Int][x^3/(-4*E^5 - x*(4 + x + Log[6]) - 4*Log[-5 + x])^3, x] + 3200*
Defer[Int][1/((5 - x)*(4*E^5 + x^2 + 4*x*(1 + Log[6]/4) + 4*Log[-5 + x])^3), x] - 32*(4 + Log[6])*Defer[Int][x
^2/(4*E^5 + x^2 + 4*x*(1 + Log[6]/4) + 4*Log[-5 + x])^3, x] + 32*Defer[Int][x/(4*E^5 + x^2 + 4*x*(1 + Log[6]/4
) + 4*Log[-5 + x])^2, x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-128 x^2+160 x^3-32 x^4+e^5 \left (-640 x+128 x^2\right )+\left (-640 x+128 x^2\right ) \log (-5+x)}{-320 x^3-176 x^4-12 x^5+7 x^6+x^7+e^{15} (-320+64 x)+e^{10} \left (-960 x-48 x^2+48 x^3\right )+e^5 \left (-960 x^2-288 x^3+36 x^4+12 x^5\right )+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )\right ) \log (2)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )\right ) \log ^2(2)+\left (-240 x^3-72 x^4+9 x^5+3 x^6+e^{10} \left (-240 x+48 x^2\right )+e^5 \left (-480 x^2-24 x^3+24 x^4\right )+\left (-120 x^3-6 x^4+6 x^5+e^5 \left (-120 x^2+24 x^3\right )\right ) \log (2)+\left (-15 x^3+3 x^4\right ) \log ^2(2)\right ) \log (3)+\left (-60 x^3-3 x^4+3 x^5+e^5 \left (-60 x^2+12 x^3\right )+\left (-15 x^3+3 x^4\right ) \log (2)\right ) \log ^2(3)+\left (-5 x^3+x^4\right ) \left (\log ^3(2)+\log ^3(3)\right )+\left (-960 x^2-288 x^3+36 x^4+12 x^5+e^{10} (-960+192 x)+e^5 \left (-1920 x-96 x^2+96 x^3\right )+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )\right ) \log (2)+\left (-60 x^2+12 x^3\right ) \log ^2(2)+\left (-480 x^2-24 x^3+24 x^4+e^5 \left (-480 x+96 x^2\right )+\left (-120 x^2+24 x^3\right ) \log (2)\right ) \log (3)+\left (-60 x^2+12 x^3\right ) \log ^2(3)\right ) \log (-5+x)+\left (-960 x-48 x^2+48 x^3+e^5 (-960+192 x)+\left (-240 x+48 x^2\right ) \log (2)+\left (-240 x+48 x^2\right ) \log (3)\right ) \log ^2(-5+x)+(-320+64 x) \log ^3(-5+x)} \, dx\\ &=\int \frac {32 x \left (-4 e^5 (-5+x)+x \left (4-5 x+x^2\right )-4 (-5+x) \log (-5+x)\right )}{(5-x) \left (4 e^5+x (4+x+\log (6))+4 \log (-5+x)\right )^3} \, dx\\ &=32 \int \frac {x \left (-4 e^5 (-5+x)+x \left (4-5 x+x^2\right )-4 (-5+x) \log (-5+x)\right )}{(5-x) \left (4 e^5+x (4+x+\log (6))+4 \log (-5+x)\right )^3} \, dx\\ &=32 \int \left (\frac {x^2 \left (-16+2 x^2-x (6-\log (6))-5 \log (6)\right )}{(5-x) \left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^3}+\frac {x}{\left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^2}\right ) \, dx\\ &=32 \int \frac {x^2 \left (-16+2 x^2-x (6-\log (6))-5 \log (6)\right )}{(5-x) \left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^3} \, dx+32 \int \frac {x}{\left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^2} \, dx\\ &=32 \int \frac {x}{\left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^2} \, dx+32 \int \left (\frac {20}{\left (-4 e^5-x^2-4 x \left (1+\frac {\log (6)}{4}\right )-4 \log (-5+x)\right )^3}+\frac {4 x}{\left (-4 e^5-x^2-4 x \left (1+\frac {\log (6)}{4}\right )-4 \log (-5+x)\right )^3}+\frac {2 x^3}{\left (-4 e^5-x^2-4 x \left (1+\frac {\log (6)}{4}\right )-4 \log (-5+x)\right )^3}+\frac {100}{(5-x) \left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^3}+\frac {x^2 (-4-\log (6))}{\left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^3}\right ) \, dx\\ &=32 \int \frac {x}{\left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^2} \, dx+64 \int \frac {x^3}{\left (-4 e^5-x^2-4 x \left (1+\frac {\log (6)}{4}\right )-4 \log (-5+x)\right )^3} \, dx+128 \int \frac {x}{\left (-4 e^5-x^2-4 x \left (1+\frac {\log (6)}{4}\right )-4 \log (-5+x)\right )^3} \, dx+640 \int \frac {1}{\left (-4 e^5-x^2-4 x \left (1+\frac {\log (6)}{4}\right )-4 \log (-5+x)\right )^3} \, dx+3200 \int \frac {1}{(5-x) \left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^3} \, dx-(32 (4+\log (6))) \int \frac {x^2}{\left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^3} \, dx\\ &=32 \int \frac {x}{\left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^2} \, dx+64 \int \frac {x^3}{\left (-4 e^5-x (4+x+\log (6))-4 \log (-5+x)\right )^3} \, dx+128 \int \frac {x}{\left (-4 e^5-x (4+x+\log (6))-4 \log (-5+x)\right )^3} \, dx+640 \int \frac {1}{\left (-4 e^5-x (4+x+\log (6))-4 \log (-5+x)\right )^3} \, dx+3200 \int \frac {1}{(5-x) \left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^3} \, dx-(32 (4+\log (6))) \int \frac {x^2}{\left (4 e^5+x^2+4 x \left (1+\frac {\log (6)}{4}\right )+4 \log (-5+x)\right )^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 4.19, size = 26, normalized size = 1.00 \begin {gather*} \frac {16 x^2}{\left (4 e^5+x (4+x+\log (6))+4 \log (-5+x)\right )^2} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-128*x^2 + 160*x^3 - 32*x^4 + E^5*(-640*x + 128*x^2) + (-640*x + 128*x^2)*Log[-5 + x])/(-320*x^3 -
176*x^4 - 12*x^5 + 7*x^6 + x^7 + E^15*(-320 + 64*x) + E^10*(-960*x - 48*x^2 + 48*x^3) + E^5*(-960*x^2 - 288*x^
3 + 36*x^4 + 12*x^5) + (-240*x^3 - 72*x^4 + 9*x^5 + 3*x^6 + E^10*(-240*x + 48*x^2) + E^5*(-480*x^2 - 24*x^3 +
24*x^4))*Log[2] + (-60*x^3 - 3*x^4 + 3*x^5 + E^5*(-60*x^2 + 12*x^3))*Log[2]^2 + (-5*x^3 + x^4)*Log[2]^3 + (-24
0*x^3 - 72*x^4 + 9*x^5 + 3*x^6 + E^10*(-240*x + 48*x^2) + E^5*(-480*x^2 - 24*x^3 + 24*x^4) + (-120*x^3 - 6*x^4
+ 6*x^5 + E^5*(-120*x^2 + 24*x^3))*Log[2] + (-15*x^3 + 3*x^4)*Log[2]^2)*Log[3] + (-60*x^3 - 3*x^4 + 3*x^5 + E
^5*(-60*x^2 + 12*x^3) + (-15*x^3 + 3*x^4)*Log[2])*Log[3]^2 + (-5*x^3 + x^4)*Log[3]^3 + (-960*x^2 - 288*x^3 + 3
6*x^4 + 12*x^5 + E^10*(-960 + 192*x) + E^5*(-1920*x - 96*x^2 + 96*x^3) + (-480*x^2 - 24*x^3 + 24*x^4 + E^5*(-4
80*x + 96*x^2))*Log[2] + (-60*x^2 + 12*x^3)*Log[2]^2 + (-480*x^2 - 24*x^3 + 24*x^4 + E^5*(-480*x + 96*x^2) + (
-120*x^2 + 24*x^3)*Log[2])*Log[3] + (-60*x^2 + 12*x^3)*Log[3]^2)*Log[-5 + x] + (-960*x - 48*x^2 + 48*x^3 + E^5
*(-960 + 192*x) + (-240*x + 48*x^2)*Log[2] + (-240*x + 48*x^2)*Log[3])*Log[-5 + x]^2 + (-320 + 64*x)*Log[-5 +
x]^3),x]
[Out]
(16*x^2)/(4*E^5 + x*(4 + x + Log[6]) + 4*Log[-5 + x])^2
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fricas [B] time = 0.56, size = 127, normalized size = 4.88 \begin {gather*} \frac {16 \, x^{2}}{x^{4} + x^{2} \log \relax (3)^{2} + x^{2} \log \relax (2)^{2} + 8 \, x^{3} + 16 \, x^{2} + 8 \, {\left (x^{2} + 4 \, x\right )} e^{5} + 2 \, {\left (x^{3} + x^{2} \log \relax (2) + 4 \, x^{2} + 4 \, x e^{5}\right )} \log \relax (3) + 2 \, {\left (x^{3} + 4 \, x^{2} + 4 \, x e^{5}\right )} \log \relax (2) + 8 \, {\left (x^{2} + x \log \relax (3) + x \log \relax (2) + 4 \, x + 4 \, e^{5}\right )} \log \left (x - 5\right ) + 16 \, \log \left (x - 5\right )^{2} + 16 \, e^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((128*x^2-640*x)*log(x-5)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3-128*x^2)/((64*x-320)*log(x-5)^3+((48
*x^2-240*x)*log(3)+(48*x^2-240*x)*log(2)+(192*x-960)*exp(5)+48*x^3-48*x^2-960*x)*log(x-5)^2+((12*x^3-60*x^2)*l
og(3)^2+((24*x^3-120*x^2)*log(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*log(3)+(12*x^3-60*x^2)*log(2)^2+
((96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*log(2)+(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5
+36*x^4-288*x^3-960*x^2)*log(x-5)+(x^4-5*x^3)*log(3)^3+((3*x^4-15*x^3)*log(2)+(12*x^3-60*x^2)*exp(5)+3*x^5-3*x
^4-60*x^3)*log(3)^2+((3*x^4-15*x^3)*log(2)^2+((24*x^3-120*x^2)*exp(5)+6*x^5-6*x^4-120*x^3)*log(2)+(48*x^2-240*
x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*log(3)+(x^4-5*x^3)*log(2)^3+((12*x^3-60
*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(2)^2+((48*x^2-240*x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-
72*x^4-240*x^3)*log(2)+(64*x-320)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12*x^5+36*x^4-288*x^3-960*x^2)*exp(
5)+x^7+7*x^6-12*x^5-176*x^4-320*x^3),x, algorithm="fricas")
[Out]
16*x^2/(x^4 + x^2*log(3)^2 + x^2*log(2)^2 + 8*x^3 + 16*x^2 + 8*(x^2 + 4*x)*e^5 + 2*(x^3 + x^2*log(2) + 4*x^2 +
4*x*e^5)*log(3) + 2*(x^3 + 4*x^2 + 4*x*e^5)*log(2) + 8*(x^2 + x*log(3) + x*log(2) + 4*x + 4*e^5)*log(x - 5) +
16*log(x - 5)^2 + 16*e^10)
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giac [B] time = 0.55, size = 154, normalized size = 5.92 \begin {gather*} \frac {16 \, x^{2}}{x^{4} + 2 \, x^{3} \log \relax (3) + x^{2} \log \relax (3)^{2} + 2 \, x^{3} \log \relax (2) + 2 \, x^{2} \log \relax (3) \log \relax (2) + x^{2} \log \relax (2)^{2} + 8 \, x^{3} + 8 \, x^{2} e^{5} + 8 \, x^{2} \log \relax (3) + 8 \, x e^{5} \log \relax (3) + 8 \, x^{2} \log \relax (2) + 8 \, x e^{5} \log \relax (2) + 8 \, x^{2} \log \left (x - 5\right ) + 8 \, x \log \relax (3) \log \left (x - 5\right ) + 8 \, x \log \relax (2) \log \left (x - 5\right ) + 16 \, x^{2} + 32 \, x e^{5} + 32 \, x \log \left (x - 5\right ) + 32 \, e^{5} \log \left (x - 5\right ) + 16 \, \log \left (x - 5\right )^{2} + 16 \, e^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((128*x^2-640*x)*log(x-5)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3-128*x^2)/((64*x-320)*log(x-5)^3+((48
*x^2-240*x)*log(3)+(48*x^2-240*x)*log(2)+(192*x-960)*exp(5)+48*x^3-48*x^2-960*x)*log(x-5)^2+((12*x^3-60*x^2)*l
og(3)^2+((24*x^3-120*x^2)*log(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*log(3)+(12*x^3-60*x^2)*log(2)^2+
((96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*log(2)+(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5
+36*x^4-288*x^3-960*x^2)*log(x-5)+(x^4-5*x^3)*log(3)^3+((3*x^4-15*x^3)*log(2)+(12*x^3-60*x^2)*exp(5)+3*x^5-3*x
^4-60*x^3)*log(3)^2+((3*x^4-15*x^3)*log(2)^2+((24*x^3-120*x^2)*exp(5)+6*x^5-6*x^4-120*x^3)*log(2)+(48*x^2-240*
x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*log(3)+(x^4-5*x^3)*log(2)^3+((12*x^3-60
*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(2)^2+((48*x^2-240*x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-
72*x^4-240*x^3)*log(2)+(64*x-320)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12*x^5+36*x^4-288*x^3-960*x^2)*exp(
5)+x^7+7*x^6-12*x^5-176*x^4-320*x^3),x, algorithm="giac")
[Out]
16*x^2/(x^4 + 2*x^3*log(3) + x^2*log(3)^2 + 2*x^3*log(2) + 2*x^2*log(3)*log(2) + x^2*log(2)^2 + 8*x^3 + 8*x^2*
e^5 + 8*x^2*log(3) + 8*x*e^5*log(3) + 8*x^2*log(2) + 8*x*e^5*log(2) + 8*x^2*log(x - 5) + 8*x*log(3)*log(x - 5)
+ 8*x*log(2)*log(x - 5) + 16*x^2 + 32*x*e^5 + 32*x*log(x - 5) + 32*e^5*log(x - 5) + 16*log(x - 5)^2 + 16*e^10
)
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maple [A] time = 0.12, size = 33, normalized size = 1.27
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\(\frac {16 x^{2}}{\left (x \ln \relax (2)+x \ln \relax (3)+x^{2}+4 \,{\mathrm e}^{5}+4 \ln \left (x -5\right )+4 x \right )^{2}}\) |
\(33\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((128*x^2-640*x)*ln(x-5)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3-128*x^2)/((64*x-320)*ln(x-5)^3+((48*x^2-240
*x)*ln(3)+(48*x^2-240*x)*ln(2)+(192*x-960)*exp(5)+48*x^3-48*x^2-960*x)*ln(x-5)^2+((12*x^3-60*x^2)*ln(3)^2+((24
*x^3-120*x^2)*ln(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*ln(3)+(12*x^3-60*x^2)*ln(2)^2+((96*x^2-480*x)
*exp(5)+24*x^4-24*x^3-480*x^2)*ln(2)+(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5+36*x^4-288*x^3-
960*x^2)*ln(x-5)+(x^4-5*x^3)*ln(3)^3+((3*x^4-15*x^3)*ln(2)+(12*x^3-60*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*ln(3)^2+
((3*x^4-15*x^3)*ln(2)^2+((24*x^3-120*x^2)*exp(5)+6*x^5-6*x^4-120*x^3)*ln(2)+(48*x^2-240*x)*exp(5)^2+(24*x^4-24
*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*ln(3)+(x^4-5*x^3)*ln(2)^3+((12*x^3-60*x^2)*exp(5)+3*x^5-3*x^4
-60*x^3)*ln(2)^2+((48*x^2-240*x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*ln(2)+(64
*x-320)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12*x^5+36*x^4-288*x^3-960*x^2)*exp(5)+x^7+7*x^6-12*x^5-176*x^
4-320*x^3),x,method=_RETURNVERBOSE)
[Out]
16*x^2/(x*ln(2)+x*ln(3)+x^2+4*exp(5)+4*ln(x-5)+4*x)^2
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maxima [B] time = 0.62, size = 97, normalized size = 3.73 \begin {gather*} \frac {16 \, x^{2}}{x^{4} + 2 \, x^{3} {\left (\log \relax (3) + \log \relax (2) + 4\right )} + {\left (\log \relax (3)^{2} + 2 \, {\left (\log \relax (3) + 4\right )} \log \relax (2) + \log \relax (2)^{2} + 8 \, e^{5} + 8 \, \log \relax (3) + 16\right )} x^{2} + 8 \, x {\left (\log \relax (3) + \log \relax (2) + 4\right )} e^{5} + 8 \, {\left (x^{2} + x {\left (\log \relax (3) + \log \relax (2) + 4\right )} + 4 \, e^{5}\right )} \log \left (x - 5\right ) + 16 \, \log \left (x - 5\right )^{2} + 16 \, e^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((128*x^2-640*x)*log(x-5)+(128*x^2-640*x)*exp(5)-32*x^4+160*x^3-128*x^2)/((64*x-320)*log(x-5)^3+((48
*x^2-240*x)*log(3)+(48*x^2-240*x)*log(2)+(192*x-960)*exp(5)+48*x^3-48*x^2-960*x)*log(x-5)^2+((12*x^3-60*x^2)*l
og(3)^2+((24*x^3-120*x^2)*log(2)+(96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*log(3)+(12*x^3-60*x^2)*log(2)^2+
((96*x^2-480*x)*exp(5)+24*x^4-24*x^3-480*x^2)*log(2)+(192*x-960)*exp(5)^2+(96*x^3-96*x^2-1920*x)*exp(5)+12*x^5
+36*x^4-288*x^3-960*x^2)*log(x-5)+(x^4-5*x^3)*log(3)^3+((3*x^4-15*x^3)*log(2)+(12*x^3-60*x^2)*exp(5)+3*x^5-3*x
^4-60*x^3)*log(3)^2+((3*x^4-15*x^3)*log(2)^2+((24*x^3-120*x^2)*exp(5)+6*x^5-6*x^4-120*x^3)*log(2)+(48*x^2-240*
x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-72*x^4-240*x^3)*log(3)+(x^4-5*x^3)*log(2)^3+((12*x^3-60
*x^2)*exp(5)+3*x^5-3*x^4-60*x^3)*log(2)^2+((48*x^2-240*x)*exp(5)^2+(24*x^4-24*x^3-480*x^2)*exp(5)+3*x^6+9*x^5-
72*x^4-240*x^3)*log(2)+(64*x-320)*exp(5)^3+(48*x^3-48*x^2-960*x)*exp(5)^2+(12*x^5+36*x^4-288*x^3-960*x^2)*exp(
5)+x^7+7*x^6-12*x^5-176*x^4-320*x^3),x, algorithm="maxima")
[Out]
16*x^2/(x^4 + 2*x^3*(log(3) + log(2) + 4) + (log(3)^2 + 2*(log(3) + 4)*log(2) + log(2)^2 + 8*e^5 + 8*log(3) +
16)*x^2 + 8*x*(log(3) + log(2) + 4)*e^5 + 8*(x^2 + x*(log(3) + log(2) + 4) + 4*e^5)*log(x - 5) + 16*log(x - 5)
^2 + 16*e^10)
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mupad [F(-1)] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \text {Hanged} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((log(x - 5)*(640*x - 128*x^2) + exp(5)*(640*x - 128*x^2) + 128*x^2 - 160*x^3 + 32*x^4)/(log(2)*(exp(10)*(2
40*x - 48*x^2) + exp(5)*(480*x^2 + 24*x^3 - 24*x^4) + 240*x^3 + 72*x^4 - 9*x^5 - 3*x^6) + log(x - 5)^2*(960*x
+ log(2)*(240*x - 48*x^2) + log(3)*(240*x - 48*x^2) + 48*x^2 - 48*x^3 - exp(5)*(192*x - 960)) - log(x - 5)^3*(
64*x - 320) + log(3)^2*(exp(5)*(60*x^2 - 12*x^3) + log(2)*(15*x^3 - 3*x^4) + 60*x^3 + 3*x^4 - 3*x^5) + log(3)*
(exp(10)*(240*x - 48*x^2) + log(2)*(exp(5)*(120*x^2 - 24*x^3) + 120*x^3 + 6*x^4 - 6*x^5) + exp(5)*(480*x^2 + 2
4*x^3 - 24*x^4) + 240*x^3 + 72*x^4 - 9*x^5 - 3*x^6 + log(2)^2*(15*x^3 - 3*x^4)) + exp(10)*(960*x + 48*x^2 - 48
*x^3) + log(2)^2*(exp(5)*(60*x^2 - 12*x^3) + 60*x^3 + 3*x^4 - 3*x^5) + log(x - 5)*(log(2)*(exp(5)*(480*x - 96*
x^2) + 480*x^2 + 24*x^3 - 24*x^4) + exp(5)*(1920*x + 96*x^2 - 96*x^3) + log(3)*(exp(5)*(480*x - 96*x^2) + log(
2)*(120*x^2 - 24*x^3) + 480*x^2 + 24*x^3 - 24*x^4) + 960*x^2 + 288*x^3 - 36*x^4 - 12*x^5 + log(2)^2*(60*x^2 -
12*x^3) + log(3)^2*(60*x^2 - 12*x^3) - exp(10)*(192*x - 960)) + 320*x^3 + 176*x^4 + 12*x^5 - 7*x^6 - x^7 + log
(2)^3*(5*x^3 - x^4) + log(3)^3*(5*x^3 - x^4) - exp(15)*(64*x - 320) + exp(5)*(960*x^2 + 288*x^3 - 36*x^4 - 12*
x^5)),x)
[Out]
\text{Hanged}
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sympy [B] time = 0.77, size = 162, normalized size = 6.23 \begin {gather*} \frac {16 x^{2}}{x^{4} + 2 x^{3} \log {\relax (2 )} + 2 x^{3} \log {\relax (3 )} + 8 x^{3} + x^{2} \log {\relax (2 )}^{2} + x^{2} \log {\relax (3 )}^{2} + 2 x^{2} \log {\relax (2 )} \log {\relax (3 )} + 8 x^{2} \log {\relax (2 )} + 8 x^{2} \log {\relax (3 )} + 16 x^{2} + 8 x^{2} e^{5} + 8 x e^{5} \log {\relax (2 )} + 8 x e^{5} \log {\relax (3 )} + 32 x e^{5} + \left (8 x^{2} + 8 x \log {\relax (2 )} + 8 x \log {\relax (3 )} + 32 x + 32 e^{5}\right ) \log {\left (x - 5 \right )} + 16 \log {\left (x - 5 \right )}^{2} + 16 e^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((128*x**2-640*x)*ln(x-5)+(128*x**2-640*x)*exp(5)-32*x**4+160*x**3-128*x**2)/((64*x-320)*ln(x-5)**3+
((48*x**2-240*x)*ln(3)+(48*x**2-240*x)*ln(2)+(192*x-960)*exp(5)+48*x**3-48*x**2-960*x)*ln(x-5)**2+((12*x**3-60
*x**2)*ln(3)**2+((24*x**3-120*x**2)*ln(2)+(96*x**2-480*x)*exp(5)+24*x**4-24*x**3-480*x**2)*ln(3)+(12*x**3-60*x
**2)*ln(2)**2+((96*x**2-480*x)*exp(5)+24*x**4-24*x**3-480*x**2)*ln(2)+(192*x-960)*exp(5)**2+(96*x**3-96*x**2-1
920*x)*exp(5)+12*x**5+36*x**4-288*x**3-960*x**2)*ln(x-5)+(x**4-5*x**3)*ln(3)**3+((3*x**4-15*x**3)*ln(2)+(12*x*
*3-60*x**2)*exp(5)+3*x**5-3*x**4-60*x**3)*ln(3)**2+((3*x**4-15*x**3)*ln(2)**2+((24*x**3-120*x**2)*exp(5)+6*x**
5-6*x**4-120*x**3)*ln(2)+(48*x**2-240*x)*exp(5)**2+(24*x**4-24*x**3-480*x**2)*exp(5)+3*x**6+9*x**5-72*x**4-240
*x**3)*ln(3)+(x**4-5*x**3)*ln(2)**3+((12*x**3-60*x**2)*exp(5)+3*x**5-3*x**4-60*x**3)*ln(2)**2+((48*x**2-240*x)
*exp(5)**2+(24*x**4-24*x**3-480*x**2)*exp(5)+3*x**6+9*x**5-72*x**4-240*x**3)*ln(2)+(64*x-320)*exp(5)**3+(48*x*
*3-48*x**2-960*x)*exp(5)**2+(12*x**5+36*x**4-288*x**3-960*x**2)*exp(5)+x**7+7*x**6-12*x**5-176*x**4-320*x**3),
x)
[Out]
16*x**2/(x**4 + 2*x**3*log(2) + 2*x**3*log(3) + 8*x**3 + x**2*log(2)**2 + x**2*log(3)**2 + 2*x**2*log(2)*log(3
) + 8*x**2*log(2) + 8*x**2*log(3) + 16*x**2 + 8*x**2*exp(5) + 8*x*exp(5)*log(2) + 8*x*exp(5)*log(3) + 32*x*exp
(5) + (8*x**2 + 8*x*log(2) + 8*x*log(3) + 32*x + 32*exp(5))*log(x - 5) + 16*log(x - 5)**2 + 16*exp(10))
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