3.50.46 \(\int \frac {216-900 x+630 x^2+72 x^3-92 x^4-x^5+3 x^6+(-18+204 x-52 x^2-20 x^3+2 x^4) \log (x)+(-11 x-x^2) \log ^2(x)+(-144+906 x-254 x^2-184 x^3+22 x^4+9 x^5+(6-108 x-8 x^2+6 x^3) \log (x)+x \log ^2(x)) \log (3+x)+(24-322 x-48 x^2+45 x^3+9 x^4+(14 x+4 x^2) \log (x)) \log ^2(3+x)+(40 x+22 x^2+3 x^3) \log ^3(3+x)}{-27 x+27 x^2-9 x^3+x^4+(27 x-18 x^2+3 x^3) \log (3+x)+(-9 x+3 x^2) \log ^2(3+x)+x \log ^3(3+x)} \, dx\)

Optimal. Leaf size=23 \[ (3+x) \left (4+x+\frac {x+\log (x)}{-3+x+\log (3+x)}\right )^2 \]

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Rubi [F]  time = 4.12, 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 {216-900 x+630 x^2+72 x^3-92 x^4-x^5+3 x^6+\left (-18+204 x-52 x^2-20 x^3+2 x^4\right ) \log (x)+\left (-11 x-x^2\right ) \log ^2(x)+\left (-144+906 x-254 x^2-184 x^3+22 x^4+9 x^5+\left (6-108 x-8 x^2+6 x^3\right ) \log (x)+x \log ^2(x)\right ) \log (3+x)+\left (24-322 x-48 x^2+45 x^3+9 x^4+\left (14 x+4 x^2\right ) \log (x)\right ) \log ^2(3+x)+\left (40 x+22 x^2+3 x^3\right ) \log ^3(3+x)}{-27 x+27 x^2-9 x^3+x^4+\left (27 x-18 x^2+3 x^3\right ) \log (3+x)+\left (-9 x+3 x^2\right ) \log ^2(3+x)+x \log ^3(3+x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(216 - 900*x + 630*x^2 + 72*x^3 - 92*x^4 - x^5 + 3*x^6 + (-18 + 204*x - 52*x^2 - 20*x^3 + 2*x^4)*Log[x] +
(-11*x - x^2)*Log[x]^2 + (-144 + 906*x - 254*x^2 - 184*x^3 + 22*x^4 + 9*x^5 + (6 - 108*x - 8*x^2 + 6*x^3)*Log[
x] + x*Log[x]^2)*Log[3 + x] + (24 - 322*x - 48*x^2 + 45*x^3 + 9*x^4 + (14*x + 4*x^2)*Log[x])*Log[3 + x]^2 + (4
0*x + 22*x^2 + 3*x^3)*Log[3 + x]^3)/(-27*x + 27*x^2 - 9*x^3 + x^4 + (27*x - 18*x^2 + 3*x^3)*Log[3 + x] + (-9*x
+ 3*x^2)*Log[3 + x]^2 + x*Log[3 + x]^3),x]

[Out]

40*x + 11*x^2 + x^3 - 8*Defer[Int][x^2/(-3 + x + Log[3 + x])^3, x] - 2*Defer[Int][x^3/(-3 + x + Log[3 + x])^3,
x] - 16*Defer[Int][(x*Log[x])/(-3 + x + Log[3 + x])^3, x] - 4*Defer[Int][(x^2*Log[x])/(-3 + x + Log[3 + x])^3
, x] - 8*Defer[Int][Log[x]^2/(-3 + x + Log[3 + x])^3, x] - 2*Defer[Int][(x*Log[x]^2)/(-3 + x + Log[3 + x])^3,
x] + 6*Defer[Int][(-3 + x + Log[3 + x])^(-2), x] - 24*Defer[Int][x/(-3 + x + Log[3 + x])^2, x] - 13*Defer[Int]
[x^2/(-3 + x + Log[3 + x])^2, x] - 2*Defer[Int][x^3/(-3 + x + Log[3 + x])^2, x] - 24*Defer[Int][Log[x]/(-3 + x
+ Log[3 + x])^2, x] + 6*Defer[Int][Log[x]/(x*(-3 + x + Log[3 + x])^2), x] - 12*Defer[Int][(x*Log[x])/(-3 + x
+ Log[3 + x])^2, x] - 2*Defer[Int][(x^2*Log[x])/(-3 + x + Log[3 + x])^2, x] + Defer[Int][Log[x]^2/(-3 + x + Lo
g[3 + x])^2, x] + 38*Defer[Int][(-3 + x + Log[3 + x])^(-1), x] + 24*Defer[Int][1/(x*(-3 + x + Log[3 + x])), x]
+ 30*Defer[Int][x/(-3 + x + Log[3 + x]), x] + 6*Defer[Int][x^2/(-3 + x + Log[3 + x]), x] + 14*Defer[Int][Log[
x]/(-3 + x + Log[3 + x]), x] + 4*Defer[Int][(x*Log[x])/(-3 + x + Log[3 + x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-216+900 x-630 x^2-72 x^3+92 x^4+x^5-3 x^6-\left (-18+204 x-52 x^2-20 x^3+2 x^4\right ) \log (x)-\left (-11 x-x^2\right ) \log ^2(x)-\left (-144+906 x-254 x^2-184 x^3+22 x^4+9 x^5+\left (6-108 x-8 x^2+6 x^3\right ) \log (x)+x \log ^2(x)\right ) \log (3+x)-\left (24-322 x-48 x^2+45 x^3+9 x^4+\left (14 x+4 x^2\right ) \log (x)\right ) \log ^2(3+x)-\left (40 x+22 x^2+3 x^3\right ) \log ^3(3+x)}{x (3-x-\log (3+x))^3} \, dx\\ &=\int \left (40+22 x+3 x^2-\frac {2 (4+x) (x+\log (x))^2}{(-3+x+\log (3+x))^3}+\frac {6 x-24 x^2-13 x^3-2 x^4+6 \log (x)-24 x \log (x)-12 x^2 \log (x)-2 x^3 \log (x)+x \log ^2(x)}{x (-3+x+\log (3+x))^2}+\frac {2 \left (12+19 x+15 x^2+3 x^3+7 x \log (x)+2 x^2 \log (x)\right )}{x (-3+x+\log (3+x))}\right ) \, dx\\ &=40 x+11 x^2+x^3-2 \int \frac {(4+x) (x+\log (x))^2}{(-3+x+\log (3+x))^3} \, dx+2 \int \frac {12+19 x+15 x^2+3 x^3+7 x \log (x)+2 x^2 \log (x)}{x (-3+x+\log (3+x))} \, dx+\int \frac {6 x-24 x^2-13 x^3-2 x^4+6 \log (x)-24 x \log (x)-12 x^2 \log (x)-2 x^3 \log (x)+x \log ^2(x)}{x (-3+x+\log (3+x))^2} \, dx\\ &=40 x+11 x^2+x^3-2 \int \left (\frac {4 (x+\log (x))^2}{(-3+x+\log (3+x))^3}+\frac {x (x+\log (x))^2}{(-3+x+\log (3+x))^3}\right ) \, dx+2 \int \left (\frac {19}{-3+x+\log (3+x)}+\frac {12}{x (-3+x+\log (3+x))}+\frac {15 x}{-3+x+\log (3+x)}+\frac {3 x^2}{-3+x+\log (3+x)}+\frac {7 \log (x)}{-3+x+\log (3+x)}+\frac {2 x \log (x)}{-3+x+\log (3+x)}\right ) \, dx+\int \left (\frac {6}{(-3+x+\log (3+x))^2}-\frac {24 x}{(-3+x+\log (3+x))^2}-\frac {13 x^2}{(-3+x+\log (3+x))^2}-\frac {2 x^3}{(-3+x+\log (3+x))^2}-\frac {24 \log (x)}{(-3+x+\log (3+x))^2}+\frac {6 \log (x)}{x (-3+x+\log (3+x))^2}-\frac {12 x \log (x)}{(-3+x+\log (3+x))^2}-\frac {2 x^2 \log (x)}{(-3+x+\log (3+x))^2}+\frac {\log ^2(x)}{(-3+x+\log (3+x))^2}\right ) \, dx\\ &=40 x+11 x^2+x^3-2 \int \frac {x (x+\log (x))^2}{(-3+x+\log (3+x))^3} \, dx-2 \int \frac {x^3}{(-3+x+\log (3+x))^2} \, dx-2 \int \frac {x^2 \log (x)}{(-3+x+\log (3+x))^2} \, dx+4 \int \frac {x \log (x)}{-3+x+\log (3+x)} \, dx+6 \int \frac {1}{(-3+x+\log (3+x))^2} \, dx+6 \int \frac {\log (x)}{x (-3+x+\log (3+x))^2} \, dx+6 \int \frac {x^2}{-3+x+\log (3+x)} \, dx-8 \int \frac {(x+\log (x))^2}{(-3+x+\log (3+x))^3} \, dx-12 \int \frac {x \log (x)}{(-3+x+\log (3+x))^2} \, dx-13 \int \frac {x^2}{(-3+x+\log (3+x))^2} \, dx+14 \int \frac {\log (x)}{-3+x+\log (3+x)} \, dx-24 \int \frac {x}{(-3+x+\log (3+x))^2} \, dx-24 \int \frac {\log (x)}{(-3+x+\log (3+x))^2} \, dx+24 \int \frac {1}{x (-3+x+\log (3+x))} \, dx+30 \int \frac {x}{-3+x+\log (3+x)} \, dx+38 \int \frac {1}{-3+x+\log (3+x)} \, dx+\int \frac {\log ^2(x)}{(-3+x+\log (3+x))^2} \, dx\\ &=40 x+11 x^2+x^3-2 \int \frac {x^3}{(-3+x+\log (3+x))^2} \, dx-2 \int \frac {x^2 \log (x)}{(-3+x+\log (3+x))^2} \, dx-2 \int \left (\frac {x^3}{(-3+x+\log (3+x))^3}+\frac {2 x^2 \log (x)}{(-3+x+\log (3+x))^3}+\frac {x \log ^2(x)}{(-3+x+\log (3+x))^3}\right ) \, dx+4 \int \frac {x \log (x)}{-3+x+\log (3+x)} \, dx+6 \int \frac {1}{(-3+x+\log (3+x))^2} \, dx+6 \int \frac {\log (x)}{x (-3+x+\log (3+x))^2} \, dx+6 \int \frac {x^2}{-3+x+\log (3+x)} \, dx-8 \int \left (\frac {x^2}{(-3+x+\log (3+x))^3}+\frac {2 x \log (x)}{(-3+x+\log (3+x))^3}+\frac {\log ^2(x)}{(-3+x+\log (3+x))^3}\right ) \, dx-12 \int \frac {x \log (x)}{(-3+x+\log (3+x))^2} \, dx-13 \int \frac {x^2}{(-3+x+\log (3+x))^2} \, dx+14 \int \frac {\log (x)}{-3+x+\log (3+x)} \, dx-24 \int \frac {x}{(-3+x+\log (3+x))^2} \, dx-24 \int \frac {\log (x)}{(-3+x+\log (3+x))^2} \, dx+24 \int \frac {1}{x (-3+x+\log (3+x))} \, dx+30 \int \frac {x}{-3+x+\log (3+x)} \, dx+38 \int \frac {1}{-3+x+\log (3+x)} \, dx+\int \frac {\log ^2(x)}{(-3+x+\log (3+x))^2} \, dx\\ &=40 x+11 x^2+x^3-2 \int \frac {x^3}{(-3+x+\log (3+x))^3} \, dx-2 \int \frac {x \log ^2(x)}{(-3+x+\log (3+x))^3} \, dx-2 \int \frac {x^3}{(-3+x+\log (3+x))^2} \, dx-2 \int \frac {x^2 \log (x)}{(-3+x+\log (3+x))^2} \, dx-4 \int \frac {x^2 \log (x)}{(-3+x+\log (3+x))^3} \, dx+4 \int \frac {x \log (x)}{-3+x+\log (3+x)} \, dx+6 \int \frac {1}{(-3+x+\log (3+x))^2} \, dx+6 \int \frac {\log (x)}{x (-3+x+\log (3+x))^2} \, dx+6 \int \frac {x^2}{-3+x+\log (3+x)} \, dx-8 \int \frac {x^2}{(-3+x+\log (3+x))^3} \, dx-8 \int \frac {\log ^2(x)}{(-3+x+\log (3+x))^3} \, dx-12 \int \frac {x \log (x)}{(-3+x+\log (3+x))^2} \, dx-13 \int \frac {x^2}{(-3+x+\log (3+x))^2} \, dx+14 \int \frac {\log (x)}{-3+x+\log (3+x)} \, dx-16 \int \frac {x \log (x)}{(-3+x+\log (3+x))^3} \, dx-24 \int \frac {x}{(-3+x+\log (3+x))^2} \, dx-24 \int \frac {\log (x)}{(-3+x+\log (3+x))^2} \, dx+24 \int \frac {1}{x (-3+x+\log (3+x))} \, dx+30 \int \frac {x}{-3+x+\log (3+x)} \, dx+38 \int \frac {1}{-3+x+\log (3+x)} \, dx+\int \frac {\log ^2(x)}{(-3+x+\log (3+x))^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.10, size = 52, normalized size = 2.26 \begin {gather*} 40 x+11 x^2+x^3+\frac {(3+x) (x+\log (x))^2}{(-3+x+\log (3+x))^2}+\frac {2 (3+x) (4+x) (x+\log (x))}{-3+x+\log (3+x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(216 - 900*x + 630*x^2 + 72*x^3 - 92*x^4 - x^5 + 3*x^6 + (-18 + 204*x - 52*x^2 - 20*x^3 + 2*x^4)*Log
[x] + (-11*x - x^2)*Log[x]^2 + (-144 + 906*x - 254*x^2 - 184*x^3 + 22*x^4 + 9*x^5 + (6 - 108*x - 8*x^2 + 6*x^3
)*Log[x] + x*Log[x]^2)*Log[3 + x] + (24 - 322*x - 48*x^2 + 45*x^3 + 9*x^4 + (14*x + 4*x^2)*Log[x])*Log[3 + x]^
2 + (40*x + 22*x^2 + 3*x^3)*Log[3 + x]^3)/(-27*x + 27*x^2 - 9*x^3 + x^4 + (27*x - 18*x^2 + 3*x^3)*Log[3 + x] +
(-9*x + 3*x^2)*Log[3 + x]^2 + x*Log[3 + x]^3),x]

[Out]

40*x + 11*x^2 + x^3 + ((3 + x)*(x + Log[x])^2)/(-3 + x + Log[3 + x])^2 + (2*(3 + x)*(4 + x)*(x + Log[x]))/(-3
+ x + Log[3 + x])

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fricas [B]  time = 0.93, size = 126, normalized size = 5.48 \begin {gather*} \frac {x^{5} + 7 \, x^{4} - 8 \, x^{3} + {\left (x^{3} + 11 \, x^{2} + 40 \, x\right )} \log \left (x + 3\right )^{2} + {\left (x + 3\right )} \log \relax (x)^{2} - 156 \, x^{2} + 2 \, {\left (x^{4} + 9 \, x^{3} + 14 \, x^{2} + {\left (x^{2} + 7 \, x + 12\right )} \log \relax (x) - 108 \, x\right )} \log \left (x + 3\right ) + 2 \, {\left (x^{3} + 5 \, x^{2} - 6 \, x - 36\right )} \log \relax (x) + 288 \, x}{x^{2} + 2 \, {\left (x - 3\right )} \log \left (x + 3\right ) + \log \left (x + 3\right )^{2} - 6 \, x + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x^3+22*x^2+40*x)*log(3+x)^3+((4*x^2+14*x)*log(x)+9*x^4+45*x^3-48*x^2-322*x+24)*log(3+x)^2+(x*log
(x)^2+(6*x^3-8*x^2-108*x+6)*log(x)+9*x^5+22*x^4-184*x^3-254*x^2+906*x-144)*log(3+x)+(-x^2-11*x)*log(x)^2+(2*x^
4-20*x^3-52*x^2+204*x-18)*log(x)+3*x^6-x^5-92*x^4+72*x^3+630*x^2-900*x+216)/(x*log(3+x)^3+(3*x^2-9*x)*log(3+x)
^2+(3*x^3-18*x^2+27*x)*log(3+x)+x^4-9*x^3+27*x^2-27*x),x, algorithm="fricas")

[Out]

(x^5 + 7*x^4 - 8*x^3 + (x^3 + 11*x^2 + 40*x)*log(x + 3)^2 + (x + 3)*log(x)^2 - 156*x^2 + 2*(x^4 + 9*x^3 + 14*x
^2 + (x^2 + 7*x + 12)*log(x) - 108*x)*log(x + 3) + 2*(x^3 + 5*x^2 - 6*x - 36)*log(x) + 288*x)/(x^2 + 2*(x - 3)
*log(x + 3) + log(x + 3)^2 - 6*x + 9)

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giac [B]  time = 0.20, size = 149, normalized size = 6.48 \begin {gather*} x^{3} + 11 \, x^{2} + 40 \, x + \frac {2 \, x^{4} + 2 \, x^{3} \log \left (x + 3\right ) + 2 \, x^{3} \log \relax (x) + 2 \, x^{2} \log \left (x + 3\right ) \log \relax (x) + 9 \, x^{3} + 14 \, x^{2} \log \left (x + 3\right ) + 10 \, x^{2} \log \relax (x) + 14 \, x \log \left (x + 3\right ) \log \relax (x) + x \log \relax (x)^{2} - 15 \, x^{2} + 24 \, x \log \left (x + 3\right ) - 12 \, x \log \relax (x) + 24 \, \log \left (x + 3\right ) \log \relax (x) + 3 \, \log \relax (x)^{2} - 72 \, x - 72 \, \log \relax (x)}{x^{2} + 2 \, x \log \left (x + 3\right ) + \log \left (x + 3\right )^{2} - 6 \, x - 6 \, \log \left (x + 3\right ) + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x^3+22*x^2+40*x)*log(3+x)^3+((4*x^2+14*x)*log(x)+9*x^4+45*x^3-48*x^2-322*x+24)*log(3+x)^2+(x*log
(x)^2+(6*x^3-8*x^2-108*x+6)*log(x)+9*x^5+22*x^4-184*x^3-254*x^2+906*x-144)*log(3+x)+(-x^2-11*x)*log(x)^2+(2*x^
4-20*x^3-52*x^2+204*x-18)*log(x)+3*x^6-x^5-92*x^4+72*x^3+630*x^2-900*x+216)/(x*log(3+x)^3+(3*x^2-9*x)*log(3+x)
^2+(3*x^3-18*x^2+27*x)*log(3+x)+x^4-9*x^3+27*x^2-27*x),x, algorithm="giac")

[Out]

x^3 + 11*x^2 + 40*x + (2*x^4 + 2*x^3*log(x + 3) + 2*x^3*log(x) + 2*x^2*log(x + 3)*log(x) + 9*x^3 + 14*x^2*log(
x + 3) + 10*x^2*log(x) + 14*x*log(x + 3)*log(x) + x*log(x)^2 - 15*x^2 + 24*x*log(x + 3) - 12*x*log(x) + 24*log
(x + 3)*log(x) + 3*log(x)^2 - 72*x - 72*log(x))/(x^2 + 2*x*log(x + 3) + log(x + 3)^2 - 6*x - 6*log(x + 3) + 9)

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maple [B]  time = 0.06, size = 93, normalized size = 4.04

method	result	size
risch	\(x^{3}+11 x^{2}+40 x +\frac {\left (2 x^{3}+2 x^{2} \ln \relax (x )+2 \ln \left (3+x \right ) x^{2}+2 \ln \relax (x ) \ln \left (3+x \right ) x +3 x^{2}+4 x \ln \relax (x )+8 x \ln \left (3+x \right )+\ln \relax (x )^{2}+8 \ln \relax (x ) \ln \left (3+x \right )-24 x -24 \ln \relax (x )\right ) \left (3+x \right )}{\left (\ln \left (3+x \right )+x -3\right )^{2}}\)	\(93\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3*x^3+22*x^2+40*x)*ln(3+x)^3+((4*x^2+14*x)*ln(x)+9*x^4+45*x^3-48*x^2-322*x+24)*ln(3+x)^2+(x*ln(x)^2+(6*x
^3-8*x^2-108*x+6)*ln(x)+9*x^5+22*x^4-184*x^3-254*x^2+906*x-144)*ln(3+x)+(-x^2-11*x)*ln(x)^2+(2*x^4-20*x^3-52*x
^2+204*x-18)*ln(x)+3*x^6-x^5-92*x^4+72*x^3+630*x^2-900*x+216)/(x*ln(3+x)^3+(3*x^2-9*x)*ln(3+x)^2+(3*x^3-18*x^2
+27*x)*ln(3+x)+x^4-9*x^3+27*x^2-27*x),x,method=_RETURNVERBOSE)

[Out]

x^3+11*x^2+40*x+(2*x^3+2*x^2*ln(x)+2*ln(3+x)*x^2+2*ln(x)*ln(3+x)*x+3*x^2+4*x*ln(x)+8*x*ln(3+x)+ln(x)^2+8*ln(x)
*ln(3+x)-24*x-24*ln(x))*(3+x)/(ln(3+x)+x-3)^2

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maxima [B]  time = 0.41, size = 126, normalized size = 5.48 \begin {gather*} \frac {x^{5} + 7 \, x^{4} - 8 \, x^{3} + {\left (x^{3} + 11 \, x^{2} + 40 \, x\right )} \log \left (x + 3\right )^{2} + {\left (x + 3\right )} \log \relax (x)^{2} - 156 \, x^{2} + 2 \, {\left (x^{4} + 9 \, x^{3} + 14 \, x^{2} + {\left (x^{2} + 7 \, x + 12\right )} \log \relax (x) - 108 \, x\right )} \log \left (x + 3\right ) + 2 \, {\left (x^{3} + 5 \, x^{2} - 6 \, x - 36\right )} \log \relax (x) + 288 \, x}{x^{2} + 2 \, {\left (x - 3\right )} \log \left (x + 3\right ) + \log \left (x + 3\right )^{2} - 6 \, x + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x^3+22*x^2+40*x)*log(3+x)^3+((4*x^2+14*x)*log(x)+9*x^4+45*x^3-48*x^2-322*x+24)*log(3+x)^2+(x*log
(x)^2+(6*x^3-8*x^2-108*x+6)*log(x)+9*x^5+22*x^4-184*x^3-254*x^2+906*x-144)*log(3+x)+(-x^2-11*x)*log(x)^2+(2*x^
4-20*x^3-52*x^2+204*x-18)*log(x)+3*x^6-x^5-92*x^4+72*x^3+630*x^2-900*x+216)/(x*log(3+x)^3+(3*x^2-9*x)*log(3+x)
^2+(3*x^3-18*x^2+27*x)*log(3+x)+x^4-9*x^3+27*x^2-27*x),x, algorithm="maxima")

[Out]

(x^5 + 7*x^4 - 8*x^3 + (x^3 + 11*x^2 + 40*x)*log(x + 3)^2 + (x + 3)*log(x)^2 - 156*x^2 + 2*(x^4 + 9*x^3 + 14*x
^2 + (x^2 + 7*x + 12)*log(x) - 108*x)*log(x + 3) + 2*(x^3 + 5*x^2 - 6*x - 36)*log(x) + 288*x)/(x^2 + 2*(x - 3)
*log(x + 3) + log(x + 3)^2 - 6*x + 9)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\ln \left (x+3\right )}^2\,\left (\ln \relax (x)\,\left (4\,x^2+14\,x\right )-322\,x-48\,x^2+45\,x^3+9\,x^4+24\right )-\ln \relax (x)\,\left (-2\,x^4+20\,x^3+52\,x^2-204\,x+18\right )-900\,x+{\ln \left (x+3\right )}^3\,\left (3\,x^3+22\,x^2+40\,x\right )-{\ln \relax (x)}^2\,\left (x^2+11\,x\right )+\ln \left (x+3\right )\,\left (906\,x+x\,{\ln \relax (x)}^2-254\,x^2-184\,x^3+22\,x^4+9\,x^5-\ln \relax (x)\,\left (-6\,x^3+8\,x^2+108\,x-6\right )-144\right )+630\,x^2+72\,x^3-92\,x^4-x^5+3\,x^6+216}{\ln \left (x+3\right )\,\left (3\,x^3-18\,x^2+27\,x\right )-27\,x-{\ln \left (x+3\right )}^2\,\left (9\,x-3\,x^2\right )+x\,{\ln \left (x+3\right )}^3+27\,x^2-9\,x^3+x^4} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x + 3)^2*(log(x)*(14*x + 4*x^2) - 322*x - 48*x^2 + 45*x^3 + 9*x^4 + 24) - log(x)*(52*x^2 - 204*x + 20
*x^3 - 2*x^4 + 18) - 900*x + log(x + 3)^3*(40*x + 22*x^2 + 3*x^3) - log(x)^2*(11*x + x^2) + log(x + 3)*(906*x
+ x*log(x)^2 - 254*x^2 - 184*x^3 + 22*x^4 + 9*x^5 - log(x)*(108*x + 8*x^2 - 6*x^3 - 6) - 144) + 630*x^2 + 72*x
^3 - 92*x^4 - x^5 + 3*x^6 + 216)/(log(x + 3)*(27*x - 18*x^2 + 3*x^3) - 27*x - log(x + 3)^2*(9*x - 3*x^2) + x*l
og(x + 3)^3 + 27*x^2 - 9*x^3 + x^4),x)

[Out]

int((log(x + 3)^2*(log(x)*(14*x + 4*x^2) - 322*x - 48*x^2 + 45*x^3 + 9*x^4 + 24) - log(x)*(52*x^2 - 204*x + 20
*x^3 - 2*x^4 + 18) - 900*x + log(x + 3)^3*(40*x + 22*x^2 + 3*x^3) - log(x)^2*(11*x + x^2) + log(x + 3)*(906*x
+ x*log(x)^2 - 254*x^2 - 184*x^3 + 22*x^4 + 9*x^5 - log(x)*(108*x + 8*x^2 - 6*x^3 - 6) - 144) + 630*x^2 + 72*x
^3 - 92*x^4 - x^5 + 3*x^6 + 216)/(log(x + 3)*(27*x - 18*x^2 + 3*x^3) - 27*x - log(x + 3)^2*(9*x - 3*x^2) + x*l
og(x + 3)^3 + 27*x^2 - 9*x^3 + x^4), x)

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sympy [B]  time = 0.46, size = 136, normalized size = 5.91 \begin {gather*} x^{3} + 11 x^{2} + 40 x + \frac {2 x^{4} + 2 x^{3} \log {\relax (x )} + 9 x^{3} + 10 x^{2} \log {\relax (x )} - 15 x^{2} + x \log {\relax (x )}^{2} - 12 x \log {\relax (x )} - 72 x + \left (2 x^{3} + 2 x^{2} \log {\relax (x )} + 14 x^{2} + 14 x \log {\relax (x )} + 24 x + 24 \log {\relax (x )}\right ) \log {\left (x + 3 \right )} + 3 \log {\relax (x )}^{2} - 72 \log {\relax (x )}}{x^{2} - 6 x + \left (2 x - 6\right ) \log {\left (x + 3 \right )} + \log {\left (x + 3 \right )}^{2} + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x**3+22*x**2+40*x)*ln(3+x)**3+((4*x**2+14*x)*ln(x)+9*x**4+45*x**3-48*x**2-322*x+24)*ln(3+x)**2+(
x*ln(x)**2+(6*x**3-8*x**2-108*x+6)*ln(x)+9*x**5+22*x**4-184*x**3-254*x**2+906*x-144)*ln(3+x)+(-x**2-11*x)*ln(x
)**2+(2*x**4-20*x**3-52*x**2+204*x-18)*ln(x)+3*x**6-x**5-92*x**4+72*x**3+630*x**2-900*x+216)/(x*ln(3+x)**3+(3*
x**2-9*x)*ln(3+x)**2+(3*x**3-18*x**2+27*x)*ln(3+x)+x**4-9*x**3+27*x**2-27*x),x)

[Out]

x**3 + 11*x**2 + 40*x + (2*x**4 + 2*x**3*log(x) + 9*x**3 + 10*x**2*log(x) - 15*x**2 + x*log(x)**2 - 12*x*log(x
) - 72*x + (2*x**3 + 2*x**2*log(x) + 14*x**2 + 14*x*log(x) + 24*x + 24*log(x))*log(x + 3) + 3*log(x)**2 - 72*l
og(x))/(x**2 - 6*x + (2*x - 6)*log(x + 3) + log(x + 3)**2 + 9)

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