3.102.66 \(\int \frac {25 x+25 x^3 \log (3)+10 x^2 \log (3) \log (625)+x \log (3) \log ^2(625)+(-25 x+25 x^2+25 x^3 \log (3)+(-5+10 x+10 x^2 \log (3)) \log (625)+(1+x \log (3)) \log ^2(625)) \log (\frac {-5+5 x+5 x^2 \log (3)+(1+x \log (3)) \log (625)}{5 x+\log (625)})}{-50 x+50 x^2+50 x^3 \log (3)+(-10+20 x+20 x^2 \log (3)) \log (625)+(2+2 x \log (3)) \log ^2(625)} \, dx\)
Optimal. Leaf size=24 \[ \frac {1}{2} x \log \left (1+x \log (3)-\frac {1}{x+\frac {\log (625)}{5}}\right ) \]
________________________________________________________________________________________
Rubi [F] time = 180.01, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
Int[(25*x + 25*x^3*Log[3] + 10*x^2*Log[3]*Log[625] + x*Log[3]*Log[625]^2 + (-25*x + 25*x^2 + 25*x^3*Log[3] + (
-5 + 10*x + 10*x^2*Log[3])*Log[625] + (1 + x*Log[3])*Log[625]^2)*Log[(-5 + 5*x + 5*x^2*Log[3] + (1 + x*Log[3])
*Log[625])/(5*x + Log[625])])/(-50*x + 50*x^2 + 50*x^3*Log[3] + (-10 + 20*x + 20*x^2*Log[3])*Log[625] + (2 + 2
*x*Log[3])*Log[625]^2),x]
[Out]
$Aborted
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [A] time = 0.07, size = 36, normalized size = 1.50 \begin {gather*} \frac {1}{2} x \log \left (\frac {-5+5 x+5 x^2 \log (3)+(1+x \log (3)) \log (625)}{5 x+\log (625)}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(25*x + 25*x^3*Log[3] + 10*x^2*Log[3]*Log[625] + x*Log[3]*Log[625]^2 + (-25*x + 25*x^2 + 25*x^3*Log[
3] + (-5 + 10*x + 10*x^2*Log[3])*Log[625] + (1 + x*Log[3])*Log[625]^2)*Log[(-5 + 5*x + 5*x^2*Log[3] + (1 + x*L
og[3])*Log[625])/(5*x + Log[625])])/(-50*x + 50*x^2 + 50*x^3*Log[3] + (-10 + 20*x + 20*x^2*Log[3])*Log[625] +
(2 + 2*x*Log[3])*Log[625]^2),x]
[Out]
(x*Log[(-5 + 5*x + 5*x^2*Log[3] + (1 + x*Log[3])*Log[625])/(5*x + Log[625])])/2
________________________________________________________________________________________
fricas [A] time = 0.86, size = 37, normalized size = 1.54 \begin {gather*} \frac {1}{2} \, x \log \left (\frac {5 \, x^{2} \log \relax (3) + 4 \, {\left (x \log \relax (3) + 1\right )} \log \relax (5) + 5 \, x - 5}{5 \, x + 4 \, \log \relax (5)}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((16*(x*log(3)+1)*log(5)^2+4*(10*x^2*log(3)+10*x-5)*log(5)+25*x^3*log(3)+25*x^2-25*x)*log((4*(x*log(
3)+1)*log(5)+5*x^2*log(3)+5*x-5)/(4*log(5)+5*x))+16*x*log(3)*log(5)^2+40*x^2*log(3)*log(5)+25*x^3*log(3)+25*x)
/(16*(2*x*log(3)+2)*log(5)^2+4*(20*x^2*log(3)+20*x-10)*log(5)+50*x^3*log(3)+50*x^2-50*x),x, algorithm="fricas"
)
[Out]
1/2*x*log((5*x^2*log(3) + 4*(x*log(3) + 1)*log(5) + 5*x - 5)/(5*x + 4*log(5)))
________________________________________________________________________________________
giac [A] time = 0.36, size = 40, normalized size = 1.67 \begin {gather*} \frac {1}{2} \, x \log \left (5 \, x^{2} \log \relax (3) + 4 \, x \log \relax (5) \log \relax (3) + 5 \, x + 4 \, \log \relax (5) - 5\right ) - \frac {1}{2} \, x \log \left (5 \, x + 4 \, \log \relax (5)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((16*(x*log(3)+1)*log(5)^2+4*(10*x^2*log(3)+10*x-5)*log(5)+25*x^3*log(3)+25*x^2-25*x)*log((4*(x*log(
3)+1)*log(5)+5*x^2*log(3)+5*x-5)/(4*log(5)+5*x))+16*x*log(3)*log(5)^2+40*x^2*log(3)*log(5)+25*x^3*log(3)+25*x)
/(16*(2*x*log(3)+2)*log(5)^2+4*(20*x^2*log(3)+20*x-10)*log(5)+50*x^3*log(3)+50*x^2-50*x),x, algorithm="giac")
[Out]
1/2*x*log(5*x^2*log(3) + 4*x*log(5)*log(3) + 5*x + 4*log(5) - 5) - 1/2*x*log(5*x + 4*log(5))
________________________________________________________________________________________
maple [A] time = 0.24, size = 38, normalized size = 1.58
|
|
|
| method |
result |
size |
|
|
|
| norman |
\(\frac {x \ln \left (\frac {4 \left (x \ln \relax (3)+1\right ) \ln \relax (5)+5 x^{2} \ln \relax (3)+5 x -5}{4 \ln \relax (5)+5 x}\right )}{2}\) |
\(38\) |
| risch |
\(\frac {x \ln \left (\frac {4 \left (x \ln \relax (3)+1\right ) \ln \relax (5)+5 x^{2} \ln \relax (3)+5 x -5}{4 \ln \relax (5)+5 x}\right )}{2}\) |
\(38\) |
| default |
\(\frac {\ln \left (\frac {4 x \ln \relax (3) \ln \relax (5)+5 x^{2} \ln \relax (3)+4 \ln \relax (5)+5 x -5}{4 \ln \relax (5)+5 x}\right ) x}{2}\) |
\(39\) |
|
|
|
| |
| |
| |
| |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((16*(x*ln(3)+1)*ln(5)^2+4*(10*x^2*ln(3)+10*x-5)*ln(5)+25*x^3*ln(3)+25*x^2-25*x)*ln((4*(x*ln(3)+1)*ln(5)+5
*x^2*ln(3)+5*x-5)/(4*ln(5)+5*x))+16*x*ln(3)*ln(5)^2+40*x^2*ln(3)*ln(5)+25*x^3*ln(3)+25*x)/(16*(2*x*ln(3)+2)*ln
(5)^2+4*(20*x^2*ln(3)+20*x-10)*ln(5)+50*x^3*ln(3)+50*x^2-50*x),x,method=_RETURNVERBOSE)
[Out]
1/2*x*ln((4*(x*ln(3)+1)*ln(5)+5*x^2*ln(3)+5*x-5)/(4*ln(5)+5*x))
________________________________________________________________________________________
maxima [B] time = 0.56, size = 961, normalized size = 40.04 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((16*(x*log(3)+1)*log(5)^2+4*(10*x^2*log(3)+10*x-5)*log(5)+25*x^3*log(3)+25*x^2-25*x)*log((4*(x*log(
3)+1)*log(5)+5*x^2*log(3)+5*x-5)/(4*log(5)+5*x))+16*x*log(3)*log(5)^2+40*x^2*log(3)*log(5)+25*x^3*log(3)+25*x)
/(16*(2*x*log(3)+2)*log(5)^2+4*(20*x^2*log(3)+20*x-10)*log(5)+50*x^3*log(3)+50*x^2-50*x),x, algorithm="maxima"
)
[Out]
-8/125*(2*log(5)*log(5*x^2*log(3) + (4*log(5)*log(3) + 5)*x + 4*log(5) - 5) - 4*log(5)*log(5*x + 4*log(5)) - (
8*log(5)^2*log(3) - 10*log(5) + 25)*log((10*x*log(3) + 4*log(5)*log(3) - sqrt(16*log(5)^2*log(3)^2 - 40*log(5)
*log(3) + 100*log(3) + 25) + 5)/(10*x*log(3) + 4*log(5)*log(3) + sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3)
+ 100*log(3) + 25) + 5))/sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3) + 100*log(3) + 25))*log(5)^2*log(3) - 2/
125*(32*log(5)^2*log(5*x + 4*log(5)) - (16*log(5)^2*log(3) + 25)*log(5*x^2*log(3) + (4*log(5)*log(3) + 5)*x +
4*log(5) - 5)/log(3) + (64*log(5)^3*log(3)^2 - 80*log(5)^2*log(3) + 300*log(5)*log(3) + 125)*log((10*x*log(3)
+ 4*log(5)*log(3) - sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3) + 100*log(3) + 25) + 5)/(10*x*log(3) + 4*log(
5)*log(3) + sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3) + 100*log(3) + 25) + 5))/(sqrt(16*log(5)^2*log(3)^2 -
40*log(5)*log(3) + 100*log(3) + 25)*log(3)))*log(5)*log(3) + 1/500*(128*log(5)^3*log(5*x + 4*log(5)) + 250*x/
log(3) - (64*log(5)^3*log(3)^2 + 200*log(5)*log(3) + 125)*log(5*x^2*log(3) + (4*log(5)*log(3) + 5)*x + 4*log(5
) - 5)/log(3)^2 + (256*log(5)^4*log(3)^3 - 320*log(5)^3*log(3)^2 + 1600*log(5)^2*log(3)^2 + 500*log(5)*log(3)
+ 1250*log(3) + 625)*log((10*x*log(3) + 4*log(5)*log(3) - sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3) + 100*l
og(3) + 25) + 5)/(10*x*log(3) + 4*log(5)*log(3) + sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3) + 100*log(3) +
25) + 5))/(sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3) + 100*log(3) + 25)*log(3)^2))*log(3) - 1/5*log(5)*log(
5*x^2*log(3) + (4*log(5)*log(3) + 5)*x + 4*log(5) - 5) + 2/5*log(5)*log(5*x + 4*log(5)) + 1/10*(8*log(5)^2*log
(3) - 10*log(5) + 25)*log((10*x*log(3) + 4*log(5)*log(3) - sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3) + 100*
log(3) + 25) + 5)/(10*x*log(3) + 4*log(5)*log(3) + sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3) + 100*log(3) +
25) + 5))/sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3) + 100*log(3) + 25) - 1/20*(16*log(5)^2*log(3)^2 - 20*(
2*log(5) - 5)*log(3) + 25)*log((10*x*log(3) + 4*log(5)*log(3) - sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3) +
100*log(3) + 25) + 5)/(10*x*log(3) + 4*log(5)*log(3) + sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3) + 100*log
(3) + 25) + 5))/(sqrt(16*log(5)^2*log(3)^2 - 40*log(5)*log(3) + 100*log(3) + 25)*log(3)) - 1/20*(10*x*log(3) -
(10*x*log(3) + 4*log(5)*log(3) + 5)*log(5*x^2*log(3) + (4*log(5)*log(3) + 5)*x + 4*log(5) - 5) + 2*(5*x*log(3
) + 4*log(5)*log(3))*log(5*x + 4*log(5)))/log(3)
________________________________________________________________________________________
mupad [B] time = 30.94, size = 37, normalized size = 1.54 \begin {gather*} \frac {x\,\ln \left (\frac {5\,x+4\,\ln \relax (5)\,\left (x\,\ln \relax (3)+1\right )+5\,x^2\,\ln \relax (3)-5}{5\,x+4\,\ln \relax (5)}\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((25*x + log((5*x + 4*log(5)*(x*log(3) + 1) + 5*x^2*log(3) - 5)/(5*x + 4*log(5)))*(25*x^3*log(3) - 25*x + 4
*log(5)*(10*x + 10*x^2*log(3) - 5) + 16*log(5)^2*(x*log(3) + 1) + 25*x^2) + 25*x^3*log(3) + 16*x*log(3)*log(5)
^2 + 40*x^2*log(3)*log(5))/(50*x^3*log(3) - 50*x + 4*log(5)*(20*x + 20*x^2*log(3) - 10) + 16*log(5)^2*(2*x*log
(3) + 2) + 50*x^2),x)
[Out]
(x*log((5*x + 4*log(5)*(x*log(3) + 1) + 5*x^2*log(3) - 5)/(5*x + 4*log(5))))/2
________________________________________________________________________________________
sympy [A] time = 0.38, size = 37, normalized size = 1.54 \begin {gather*} \frac {x \log {\left (\frac {5 x^{2} \log {\relax (3 )} + 5 x + \left (4 x \log {\relax (3 )} + 4\right ) \log {\relax (5 )} - 5}{5 x + 4 \log {\relax (5 )}} \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((16*(x*ln(3)+1)*ln(5)**2+4*(10*x**2*ln(3)+10*x-5)*ln(5)+25*x**3*ln(3)+25*x**2-25*x)*ln((4*(x*ln(3)+
1)*ln(5)+5*x**2*ln(3)+5*x-5)/(4*ln(5)+5*x))+16*x*ln(3)*ln(5)**2+40*x**2*ln(3)*ln(5)+25*x**3*ln(3)+25*x)/(16*(2
*x*ln(3)+2)*ln(5)**2+4*(20*x**2*ln(3)+20*x-10)*ln(5)+50*x**3*ln(3)+50*x**2-50*x),x)
[Out]
x*log((5*x**2*log(3) + 5*x + (4*x*log(3) + 4)*log(5) - 5)/(5*x + 4*log(5)))/2
________________________________________________________________________________________