3.9.63 \(\int \frac {24 x^2-8 x^3+64 e^4 x \log (-3+x)+e^4 (96+16 x-16 x^2) \log ^2(-3+x)+e^8 (24-8 x) \log ^4(-3+x)}{-192 x^2-32 x^3+20 x^4+4 x^5+(48 x^2-4 x^3-4 x^4) \log (5)+(-3 x^2+x^3) \log ^2(5)+(e^4 (-96 x^2+8 x^3+8 x^4)+e^4 (48 x+8 x^2-8 x^3) \log (5)+e^4 (-6 x+2 x^2) \log ^2(5)) \log ^2(-3+x)+(e^8 (-12 x^2+4 x^3)+e^8 (12 x-4 x^2) \log (5)+e^8 (-3+x) \log ^2(5)) \log ^4(-3+x)} \, dx\)

Optimal. Leaf size=29 \[ \frac {4}{2 x-\log (5)+\frac {8 x}{x+e^4 \log ^2(-3+x)}} \]

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Rubi [F]  time = 49.70, 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 {24 x^2-8 x^3+64 e^4 x \log (-3+x)+e^4 \left (96+16 x-16 x^2\right ) \log ^2(-3+x)+e^8 (24-8 x) \log ^4(-3+x)}{-192 x^2-32 x^3+20 x^4+4 x^5+\left (48 x^2-4 x^3-4 x^4\right ) \log (5)+\left (-3 x^2+x^3\right ) \log ^2(5)+\left (e^4 \left (-96 x^2+8 x^3+8 x^4\right )+e^4 \left (48 x+8 x^2-8 x^3\right ) \log (5)+e^4 \left (-6 x+2 x^2\right ) \log ^2(5)\right ) \log ^2(-3+x)+\left (e^8 \left (-12 x^2+4 x^3\right )+e^8 \left (12 x-4 x^2\right ) \log (5)+e^8 (-3+x) \log ^2(5)\right ) \log ^4(-3+x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(24*x^2 - 8*x^3 + 64*E^4*x*Log[-3 + x] + E^4*(96 + 16*x - 16*x^2)*Log[-3 + x]^2 + E^8*(24 - 8*x)*Log[-3 +
x]^4)/(-192*x^2 - 32*x^3 + 20*x^4 + 4*x^5 + (48*x^2 - 4*x^3 - 4*x^4)*Log[5] + (-3*x^2 + x^3)*Log[5]^2 + (E^4*(
-96*x^2 + 8*x^3 + 8*x^4) + E^4*(48*x + 8*x^2 - 8*x^3)*Log[5] + E^4*(-6*x + 2*x^2)*Log[5]^2)*Log[-3 + x]^2 + (E
^8*(-12*x^2 + 4*x^3) + E^8*(12*x - 4*x^2)*Log[5] + E^8*(-3 + x)*Log[5]^2)*Log[-3 + x]^4),x]

[Out]

4/(2*x - Log[5]) + (3456*Defer[Int][(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^(-2), x])/(6 - L
og[5])^2 - (96*Log[5]^2*Defer[Int][(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^(-2), x])/(6 - Lo
g[5])^2 - (32*Log[5]^2*Defer[Int][(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^(-2), x])/(6 - Log
[5]) - (1152*(3 + Log[5])*Defer[Int][(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^(-2), x])/(6 -
Log[5])^2 + (192*Log[5]*(3 + Log[5])*Defer[Int][(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^(-2)
, x])/(6 - Log[5])^2 + (32*Log[5]*(3 + Log[5])*Defer[Int][(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 +
x]^2)^(-2), x])/(6 - Log[5]) - (288*(8 - Log[5])*Log[5]*Defer[Int][1/((3 - x)*(x*(8 + 2*x - Log[5]) + E^4*(2*x
 - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5])^2 + (3456*(3 + Log[5])*Defer[Int][1/((3 - x)*(x*(8 + 2*x - Log[
5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5])^2 + (10368*Defer[Int][1/((-3 + x)*(x*(8 + 2*x - L
og[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5])^2 + (288*Log[5]*(4 + Log[5])*Defer[Int][1/((-3
 + x)*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5])^2 + (1152*Defer[Int][x/(x
*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2, x])/(6 - Log[5])^2 - (192*Log[5]*Defer[Int][x/(x*(8
 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2, x])/(6 - Log[5])^2 - (32*Log[5]*Defer[Int][x/(x*(8 + 2
*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2, x])/(6 - Log[5]) - (96*(8 - Log[5])*Log[5]^2*Defer[Int][1/
((2*x - Log[5])^2*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5]) - (16*Log[5]^
4*Defer[Int][1/((2*x - Log[5])^2*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5]
) + (32*Log[5]^3*(3 + Log[5])*Defer[Int][1/((2*x - Log[5])^2*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3
 + x]^2)^2), x])/(6 - Log[5]) - (16*Log[5]^3*(4 + Log[5])*Defer[Int][1/((2*x - Log[5])^2*(x*(8 + 2*x - Log[5])
 + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5]) - (576*(8 - Log[5])*Log[5]*Defer[Int][1/((2*x - Log[
5])*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5])^2 - (48*Log[5]^3*Defer[Int]
[1/((2*x - Log[5])*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5]) + (192*Log[5
]^2*(3 + Log[5])*Defer[Int][1/((2*x - Log[5])*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x]
)/(6 - Log[5])^2 + (64*Log[5]^2*(3 + Log[5])*Defer[Int][1/((2*x - Log[5])*(x*(8 + 2*x - Log[5]) + E^4*(2*x - L
og[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5]) - (96*Log[5]^2*(4 + Log[5])*Defer[Int][1/((2*x - Log[5])*(x*(8 + 2*
x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5])^2 - (16*Log[5]^2*(4 + Log[5])*Defer[Int][
1/((2*x - Log[5])*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5]) + (96*Log[5]^
3*Defer[Int][1/((-2*x + Log[5])*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5])
^2 + (2304*E^4*Defer[Int][Log[-3 + x]/(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2, x])/(6 - Lo
g[5])^2 - (384*E^4*Log[5]*Defer[Int][Log[-3 + x]/(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2,
x])/(6 - Log[5])^2 - (64*E^4*Log[5]*Defer[Int][Log[-3 + x]/(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 +
 x]^2)^2, x])/(6 - Log[5]) + (2304*E^4*Log[5]*Defer[Int][Log[-3 + x]/((3 - x)*(x*(8 + 2*x - Log[5]) + E^4*(2*x
 - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5])^2 + (6912*E^4*Defer[Int][Log[-3 + x]/((-3 + x)*(x*(8 + 2*x - Lo
g[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5])^2 + (192*E^4*Log[5]^2*Defer[Int][Log[-3 + x]/((
-3 + x)*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - Log[5])^2 + (768*E^4*Log[5]^2*D
efer[Int][Log[-3 + x]/((2*x - Log[5])*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5])*Log[-3 + x]^2)^2), x])/(6 - L
og[5])^2 + (768*E^4*Log[5]^2*Defer[Int][Log[-3 + x]/((-2*x + Log[5])*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log[5]
)*Log[-3 + x]^2)^2), x])/(6 - Log[5])^2 + 16*Log[625]*Defer[Int][1/((2*x - Log[5])^2*(x*(8 + 2*x - Log[5]) + E
^4*(2*x - Log[5])*Log[-3 + x]^2)), x] + 32*Defer[Int][1/((2*x - Log[5])*(x*(8 + 2*x - Log[5]) + E^4*(2*x - Log
[5])*Log[-3 + x]^2)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8 \left ((-3+x) x^2-8 e^4 x \log (-3+x)+2 e^4 \left (-6-x+x^2\right ) \log ^2(-3+x)+e^8 (-3+x) \log ^4(-3+x)\right )}{(3-x) \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )^2} \, dx\\ &=8 \int \frac {(-3+x) x^2-8 e^4 x \log (-3+x)+2 e^4 \left (-6-x+x^2\right ) \log ^2(-3+x)+e^8 (-3+x) \log ^4(-3+x)}{(3-x) \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )^2} \, dx\\ &=8 \int \left (-\frac {1}{(2 x-\log (5))^2}+\frac {4 x \left (-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)\right )}{(3-x) (2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2}+\frac {8 x+\log (625)}{(2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )}\right ) \, dx\\ &=\frac {4}{2 x-\log (5)}+8 \int \frac {8 x+\log (625)}{(2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )} \, dx+32 \int \frac {x \left (-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)\right )}{(3-x) (2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2} \, dx\\ &=\frac {4}{2 x-\log (5)}+8 \int \frac {8 x+\log (625)}{(2 x-\log (5))^2 \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )} \, dx+32 \int \frac {x \left (-\left ((-3+x) \left (4 x^2-4 x \log (5)+(-8+\log (5)) \log (5)\right )\right )-2 e^4 (-2 x+\log (5))^2 \log (-3+x)\right )}{(3-x) (2 x-\log (5))^2 \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )^2} \, dx\\ &=\frac {4}{2 x-\log (5)}+8 \int \left (\frac {4}{(2 x-\log (5)) \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )}+\frac {2 \log (625)}{(2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )}\right ) \, dx+32 \int \left (\frac {3 \left (-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)\right )}{(3-x) (6-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2}+\frac {6 \left (-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)\right )}{(6-\log (5))^2 (2 x-\log (5)) \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2}+\frac {\log (5) \left (-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)\right )}{(6-\log (5)) (2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2}\right ) \, dx\\ &=\frac {4}{2 x-\log (5)}+32 \int \frac {1}{(2 x-\log (5)) \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )} \, dx+\frac {96 \int \frac {-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)}{(3-x) \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2} \, dx}{(6-\log (5))^2}+\frac {192 \int \frac {-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)}{(2 x-\log (5)) \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2} \, dx}{(6-\log (5))^2}+\frac {(32 \log (5)) \int \frac {-4 x^3+12 x^2 \left (1+\frac {\log (5)}{3}\right )-24 \left (1-\frac {\log (5)}{8}\right ) \log (5)-4 x \left (1+\frac {\log (5)}{4}\right ) \log (5)-8 e^4 x^2 \log (-3+x)+8 e^4 x \log (5) \log (-3+x)-2 e^4 \log ^2(5) \log (-3+x)}{(2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )^2} \, dx}{6-\log (5)}+(16 \log (625)) \int \frac {1}{(2 x-\log (5))^2 \left (2 x^2+8 x \left (1-\frac {\log (5)}{8}\right )+2 e^4 x \log ^2(-3+x)-e^4 \log (5) \log ^2(-3+x)\right )} \, dx\\ &=\frac {4}{2 x-\log (5)}+32 \int \frac {1}{(2 x-\log (5)) \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )} \, dx+\frac {96 \int \frac {-\left ((-3+x) \left (4 x^2-4 x \log (5)+(-8+\log (5)) \log (5)\right )\right )-2 e^4 (-2 x+\log (5))^2 \log (-3+x)}{(3-x) \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )^2} \, dx}{(6-\log (5))^2}+\frac {192 \int \frac {-\left ((-3+x) \left (4 x^2-4 x \log (5)+(-8+\log (5)) \log (5)\right )\right )-2 e^4 (-2 x+\log (5))^2 \log (-3+x)}{(2 x-\log (5)) \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )^2} \, dx}{(6-\log (5))^2}+\frac {(32 \log (5)) \int \frac {-\left ((-3+x) \left (4 x^2-4 x \log (5)+(-8+\log (5)) \log (5)\right )\right )-2 e^4 (-2 x+\log (5))^2 \log (-3+x)}{(2 x-\log (5))^2 \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )^2} \, dx}{6-\log (5)}+(16 \log (625)) \int \frac {1}{(2 x-\log (5))^2 \left (x (8+2 x-\log (5))+e^4 (2 x-\log (5)) \log ^2(-3+x)\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 48, normalized size = 1.66 \begin {gather*} \frac {8 \left (x+e^4 \log ^2(-3+x)\right )}{2 x (8+2 x-\log (5))+2 e^4 (2 x-\log (5)) \log ^2(-3+x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(24*x^2 - 8*x^3 + 64*E^4*x*Log[-3 + x] + E^4*(96 + 16*x - 16*x^2)*Log[-3 + x]^2 + E^8*(24 - 8*x)*Log
[-3 + x]^4)/(-192*x^2 - 32*x^3 + 20*x^4 + 4*x^5 + (48*x^2 - 4*x^3 - 4*x^4)*Log[5] + (-3*x^2 + x^3)*Log[5]^2 +
(E^4*(-96*x^2 + 8*x^3 + 8*x^4) + E^4*(48*x + 8*x^2 - 8*x^3)*Log[5] + E^4*(-6*x + 2*x^2)*Log[5]^2)*Log[-3 + x]^
2 + (E^8*(-12*x^2 + 4*x^3) + E^8*(12*x - 4*x^2)*Log[5] + E^8*(-3 + x)*Log[5]^2)*Log[-3 + x]^4),x]

[Out]

(8*(x + E^4*Log[-3 + x]^2))/(2*x*(8 + 2*x - Log[5]) + 2*E^4*(2*x - Log[5])*Log[-3 + x]^2)

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fricas [A]  time = 0.70, size = 48, normalized size = 1.66 \begin {gather*} \frac {4 \, {\left (e^{4} \log \left (x - 3\right )^{2} + x\right )}}{{\left (2 \, x e^{4} - e^{4} \log \relax (5)\right )} \log \left (x - 3\right )^{2} + 2 \, x^{2} - x \log \relax (5) + 8 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-8*x+24)*exp(4)^2*log(x-3)^4+(-16*x^2+16*x+96)*exp(4)*log(x-3)^2+64*x*exp(4)*log(x-3)-8*x^3+24*x^2
)/(((x-3)*exp(4)^2*log(5)^2+(-4*x^2+12*x)*exp(4)^2*log(5)+(4*x^3-12*x^2)*exp(4)^2)*log(x-3)^4+((2*x^2-6*x)*exp
(4)*log(5)^2+(-8*x^3+8*x^2+48*x)*exp(4)*log(5)+(8*x^4+8*x^3-96*x^2)*exp(4))*log(x-3)^2+(x^3-3*x^2)*log(5)^2+(-
4*x^4-4*x^3+48*x^2)*log(5)+4*x^5+20*x^4-32*x^3-192*x^2),x, algorithm="fricas")

[Out]

4*(e^4*log(x - 3)^2 + x)/((2*x*e^4 - e^4*log(5))*log(x - 3)^2 + 2*x^2 - x*log(5) + 8*x)

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giac [B]  time = 164.41, size = 109, normalized size = 3.76 \begin {gather*} \frac {4 \, {\left (2 \, x e^{4} \log \left (x - 3\right )^{2} - e^{4} \log \relax (5) \log \left (x - 3\right )^{2} + 2 \, x^{2} - x \log \relax (5) - 8 \, x\right )}}{4 \, x^{2} e^{4} \log \left (x - 3\right )^{2} - 4 \, x e^{4} \log \relax (5) \log \left (x - 3\right )^{2} + e^{4} \log \relax (5)^{2} \log \left (x - 3\right )^{2} + 4 \, x^{3} - 4 \, x^{2} \log \relax (5) + x \log \relax (5)^{2} + 16 \, x^{2} - 8 \, x \log \relax (5)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-8*x+24)*exp(4)^2*log(x-3)^4+(-16*x^2+16*x+96)*exp(4)*log(x-3)^2+64*x*exp(4)*log(x-3)-8*x^3+24*x^2
)/(((x-3)*exp(4)^2*log(5)^2+(-4*x^2+12*x)*exp(4)^2*log(5)+(4*x^3-12*x^2)*exp(4)^2)*log(x-3)^4+((2*x^2-6*x)*exp
(4)*log(5)^2+(-8*x^3+8*x^2+48*x)*exp(4)*log(5)+(8*x^4+8*x^3-96*x^2)*exp(4))*log(x-3)^2+(x^3-3*x^2)*log(5)^2+(-
4*x^4-4*x^3+48*x^2)*log(5)+4*x^5+20*x^4-32*x^3-192*x^2),x, algorithm="giac")

[Out]

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

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maple [B]  time = 0.08, size = 60, normalized size = 2.07




method result size



risch \(-\frac {4}{\ln \relax (5)-2 x}-\frac {32 x}{\left (\ln \relax (5)-2 x \right ) \left (\ln \left (x -3\right )^{2} \ln \relax (5) {\mathrm e}^{4}-2 \,{\mathrm e}^{4} \ln \left (x -3\right )^{2} x +x \ln \relax (5)-2 x^{2}-8 x \right )}\) \(60\)



Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-8*x+24)*exp(4)^2*ln(x-3)^4+(-16*x^2+16*x+96)*exp(4)*ln(x-3)^2+64*x*exp(4)*ln(x-3)-8*x^3+24*x^2)/(((x-3)
*exp(4)^2*ln(5)^2+(-4*x^2+12*x)*exp(4)^2*ln(5)+(4*x^3-12*x^2)*exp(4)^2)*ln(x-3)^4+((2*x^2-6*x)*exp(4)*ln(5)^2+
(-8*x^3+8*x^2+48*x)*exp(4)*ln(5)+(8*x^4+8*x^3-96*x^2)*exp(4))*ln(x-3)^2+(x^3-3*x^2)*ln(5)^2+(-4*x^4-4*x^3+48*x
^2)*ln(5)+4*x^5+20*x^4-32*x^3-192*x^2),x,method=_RETURNVERBOSE)

[Out]

-4/(ln(5)-2*x)-32*x/(ln(5)-2*x)/(ln(x-3)^2*ln(5)*exp(4)-2*exp(4)*ln(x-3)^2*x+x*ln(5)-2*x^2-8*x)

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maxima [B]  time = 0.86, size = 89, normalized size = 3.07 \begin {gather*} \frac {4 \, {\left ({\left (2 \, x e^{4} - e^{4} \log \relax (5)\right )} \log \left (x - 3\right )^{2} + 2 \, x^{2} - x \log \relax (5)\right )}}{4 \, x^{3} - 4 \, x^{2} {\left (\log \relax (5) - 4\right )} + {\left (4 \, x^{2} e^{4} - 4 \, x e^{4} \log \relax (5) + e^{4} \log \relax (5)^{2}\right )} \log \left (x - 3\right )^{2} + {\left (\log \relax (5)^{2} - 8 \, \log \relax (5)\right )} x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-8*x+24)*exp(4)^2*log(x-3)^4+(-16*x^2+16*x+96)*exp(4)*log(x-3)^2+64*x*exp(4)*log(x-3)-8*x^3+24*x^2
)/(((x-3)*exp(4)^2*log(5)^2+(-4*x^2+12*x)*exp(4)^2*log(5)+(4*x^3-12*x^2)*exp(4)^2)*log(x-3)^4+((2*x^2-6*x)*exp
(4)*log(5)^2+(-8*x^3+8*x^2+48*x)*exp(4)*log(5)+(8*x^4+8*x^3-96*x^2)*exp(4))*log(x-3)^2+(x^3-3*x^2)*log(5)^2+(-
4*x^4-4*x^3+48*x^2)*log(5)+4*x^5+20*x^4-32*x^3-192*x^2),x, algorithm="maxima")

[Out]

4*((2*x*e^4 - e^4*log(5))*log(x - 3)^2 + 2*x^2 - x*log(5))/(4*x^3 - 4*x^2*(log(5) - 4) + (4*x^2*e^4 - 4*x*e^4*
log(5) + e^4*log(5)^2)*log(x - 3)^2 + (log(5)^2 - 8*log(5))*x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {24\,x^2-8\,x^3+64\,x\,\ln \left (x-3\right )\,{\mathrm {e}}^4-{\ln \left (x-3\right )}^4\,{\mathrm {e}}^8\,\left (8\,x-24\right )+{\ln \left (x-3\right )}^2\,{\mathrm {e}}^4\,\left (-16\,x^2+16\,x+96\right )}{\ln \relax (5)\,\left (4\,x^4+4\,x^3-48\,x^2\right )+192\,x^2+32\,x^3-20\,x^4-4\,x^5+{\ln \relax (5)}^2\,\left (3\,x^2-x^3\right )-{\ln \left (x-3\right )}^4\,\left ({\mathrm {e}}^8\,{\ln \relax (5)}^2\,\left (x-3\right )-{\mathrm {e}}^8\,\left (12\,x^2-4\,x^3\right )+{\mathrm {e}}^8\,\ln \relax (5)\,\left (12\,x-4\,x^2\right )\right )-{\ln \left (x-3\right )}^2\,\left ({\mathrm {e}}^4\,\left (8\,x^4+8\,x^3-96\,x^2\right )+{\mathrm {e}}^4\,\ln \relax (5)\,\left (-8\,x^3+8\,x^2+48\,x\right )-{\mathrm {e}}^4\,{\ln \relax (5)}^2\,\left (6\,x-2\,x^2\right )\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(24*x^2 - 8*x^3 + 64*x*log(x - 3)*exp(4) - log(x - 3)^4*exp(8)*(8*x - 24) + log(x - 3)^2*exp(4)*(16*x - 1
6*x^2 + 96))/(log(5)*(4*x^3 - 48*x^2 + 4*x^4) + 192*x^2 + 32*x^3 - 20*x^4 - 4*x^5 + log(5)^2*(3*x^2 - x^3) - l
og(x - 3)^4*(exp(8)*log(5)^2*(x - 3) - exp(8)*(12*x^2 - 4*x^3) + exp(8)*log(5)*(12*x - 4*x^2)) - log(x - 3)^2*
(exp(4)*(8*x^3 - 96*x^2 + 8*x^4) + exp(4)*log(5)*(48*x + 8*x^2 - 8*x^3) - exp(4)*log(5)^2*(6*x - 2*x^2))),x)

[Out]

int(-(24*x^2 - 8*x^3 + 64*x*log(x - 3)*exp(4) - log(x - 3)^4*exp(8)*(8*x - 24) + log(x - 3)^2*exp(4)*(16*x - 1
6*x^2 + 96))/(log(5)*(4*x^3 - 48*x^2 + 4*x^4) + 192*x^2 + 32*x^3 - 20*x^4 - 4*x^5 + log(5)^2*(3*x^2 - x^3) - l
og(x - 3)^4*(exp(8)*log(5)^2*(x - 3) - exp(8)*(12*x^2 - 4*x^3) + exp(8)*log(5)*(12*x - 4*x^2)) - log(x - 3)^2*
(exp(4)*(8*x^3 - 96*x^2 + 8*x^4) + exp(4)*log(5)*(48*x + 8*x^2 - 8*x^3) - exp(4)*log(5)^2*(6*x - 2*x^2))), x)

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sympy [B]  time = 0.59, size = 78, normalized size = 2.69 \begin {gather*} - \frac {32 x}{4 x^{3} - 4 x^{2} \log {\relax (5 )} + 16 x^{2} - 8 x \log {\relax (5 )} + x \log {\relax (5 )}^{2} + \left (4 x^{2} e^{4} - 4 x e^{4} \log {\relax (5 )} + e^{4} \log {\relax (5 )}^{2}\right ) \log {\left (x - 3 \right )}^{2}} + \frac {8}{4 x - 2 \log {\relax (5 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-8*x+24)*exp(4)**2*ln(x-3)**4+(-16*x**2+16*x+96)*exp(4)*ln(x-3)**2+64*x*exp(4)*ln(x-3)-8*x**3+24*x
**2)/(((x-3)*exp(4)**2*ln(5)**2+(-4*x**2+12*x)*exp(4)**2*ln(5)+(4*x**3-12*x**2)*exp(4)**2)*ln(x-3)**4+((2*x**2
-6*x)*exp(4)*ln(5)**2+(-8*x**3+8*x**2+48*x)*exp(4)*ln(5)+(8*x**4+8*x**3-96*x**2)*exp(4))*ln(x-3)**2+(x**3-3*x*
*2)*ln(5)**2+(-4*x**4-4*x**3+48*x**2)*ln(5)+4*x**5+20*x**4-32*x**3-192*x**2),x)

[Out]

-32*x/(4*x**3 - 4*x**2*log(5) + 16*x**2 - 8*x*log(5) + x*log(5)**2 + (4*x**2*exp(4) - 4*x*exp(4)*log(5) + exp(
4)*log(5)**2)*log(x - 3)**2) + 8/(4*x - 2*log(5))

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