3.99.8 \(\int \frac {10+22 x+4 x^2+5 x^5+x^6+(10+4 x+15 x^4+3 x^5) \log (x)+(15 x^3+3 x^4) \log ^2(x)+(5 x^2+x^3) \log ^3(x)+(10+2 x+(10+2 x+15 x^4+3 x^5) \log (x)+(30 x^3+6 x^4) \log ^2(x)+(15 x^2+3 x^3) \log ^3(x)) \log (5+x)+((15 x^3+3 x^4) \log ^2(x)+(15 x^2+3 x^3) \log ^3(x)) \log ^2(5+x)+(5 x^2+x^3) \log ^3(x) \log ^3(5+x)}{5 x^6+x^7+(15 x^5+3 x^6) \log (x)+(15 x^4+3 x^5) \log ^2(x)+(5 x^3+x^4) \log ^3(x)+((15 x^5+3 x^6) \log (x)+(30 x^4+6 x^5) \log ^2(x)+(15 x^3+3 x^4) \log ^3(x)) \log (5+x)+((15 x^4+3 x^5) \log ^2(x)+(15 x^3+3 x^4) \log ^3(x)) \log ^2(5+x)+(5 x^3+x^4) \log ^3(x) \log ^3(5+x)} \, dx\)

Optimal. Leaf size=22 \[ \log (x)-\frac {1}{\left (x^2+\log (x) (x+x \log (5+x))\right )^2} \]

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Rubi [F]  time = 4.57, 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 {10+22 x+4 x^2+5 x^5+x^6+\left (10+4 x+15 x^4+3 x^5\right ) \log (x)+\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (5 x^2+x^3\right ) \log ^3(x)+\left (10+2 x+\left (10+2 x+15 x^4+3 x^5\right ) \log (x)+\left (30 x^3+6 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^2+x^3\right ) \log ^3(x) \log ^3(5+x)}{5 x^6+x^7+\left (15 x^5+3 x^6\right ) \log (x)+\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (5 x^3+x^4\right ) \log ^3(x)+\left (\left (15 x^5+3 x^6\right ) \log (x)+\left (30 x^4+6 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^3+x^4\right ) \log ^3(x) \log ^3(5+x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(10 + 22*x + 4*x^2 + 5*x^5 + x^6 + (10 + 4*x + 15*x^4 + 3*x^5)*Log[x] + (15*x^3 + 3*x^4)*Log[x]^2 + (5*x^2
+ x^3)*Log[x]^3 + (10 + 2*x + (10 + 2*x + 15*x^4 + 3*x^5)*Log[x] + (30*x^3 + 6*x^4)*Log[x]^2 + (15*x^2 + 3*x^
3)*Log[x]^3)*Log[5 + x] + ((15*x^3 + 3*x^4)*Log[x]^2 + (15*x^2 + 3*x^3)*Log[x]^3)*Log[5 + x]^2 + (5*x^2 + x^3)
*Log[x]^3*Log[5 + x]^3)/(5*x^6 + x^7 + (15*x^5 + 3*x^6)*Log[x] + (15*x^4 + 3*x^5)*Log[x]^2 + (5*x^3 + x^4)*Log
[x]^3 + ((15*x^5 + 3*x^6)*Log[x] + (30*x^4 + 6*x^5)*Log[x]^2 + (15*x^3 + 3*x^4)*Log[x]^3)*Log[5 + x] + ((15*x^
4 + 3*x^5)*Log[x]^2 + (15*x^3 + 3*x^4)*Log[x]^3)*Log[5 + x]^2 + (5*x^3 + x^4)*Log[x]^3*Log[5 + x]^3),x]

[Out]

Log[x] + 2*Defer[Int][1/(x^2*(x + Log[x] + Log[x]*Log[5 + x])^3), x] - 2*Defer[Int][1/(x^2*Log[x]*(x + Log[x]
+ Log[x]*Log[5 + x])^3), x] + (2*Defer[Int][Log[x]/(x^2*(x + Log[x] + Log[x]*Log[5 + x])^3), x])/5 - (2*Defer[
Int][Log[x]/(x*(x + Log[x] + Log[x]*Log[5 + x])^3), x])/25 + (2*Defer[Int][Log[x]/((5 + x)*(x + Log[x] + Log[x
]*Log[5 + x])^3), x])/25 + 2*Defer[Int][1/(x^3*(x + Log[x] + Log[x]*Log[5 + x])^2), x] + 2*Defer[Int][1/(x^3*L
og[x]*(x + Log[x] + Log[x]*Log[5 + x])^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 x^3 (5+x) \log ^2(x) (1+\log (5+x))^2+x^2 (5+x) \log ^3(x) (1+\log (5+x))^3+(5+x) \left (2+4 x+x^5+2 \log (5+x)\right )+\log (x) \left (10+4 x+15 x^4+3 x^5+\left (10+2 x+15 x^4+3 x^5\right ) \log (5+x)\right )}{x^3 (5+x) (x+\log (x) (1+\log (5+x)))^3} \, dx\\ &=\int \left (\frac {1}{x}+\frac {2 \left (-5-x+5 \log (x)+x \log (x)+\log ^2(x)\right )}{x^2 (5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {2 (1+\log (x))}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2}\right ) \, dx\\ &=\log (x)+2 \int \frac {-5-x+5 \log (x)+x \log (x)+\log ^2(x)}{x^2 (5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1+\log (x)}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2} \, dx\\ &=\log (x)+2 \int \left (\frac {5+x-5 \log (x)-x \log (x)-\log ^2(x)}{25 x \log (x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {-5-x+5 \log (x)+x \log (x)+\log ^2(x)}{5 x^2 \log (x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {-5-x+5 \log (x)+x \log (x)+\log ^2(x)}{25 (5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3}\right ) \, dx+2 \int \left (\frac {1}{x^3 (x+\log (x)+\log (x) \log (5+x))^2}+\frac {1}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2}\right ) \, dx\\ &=\log (x)+\frac {2}{25} \int \frac {5+x-5 \log (x)-x \log (x)-\log ^2(x)}{x \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {-5-x+5 \log (x)+x \log (x)+\log ^2(x)}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{5} \int \frac {-5-x+5 \log (x)+x \log (x)+\log ^2(x)}{x^2 \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^3 (x+\log (x)+\log (x) \log (5+x))^2} \, dx+2 \int \frac {1}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2} \, dx\\ &=\log (x)+\frac {2}{25} \int \left (-\frac {1}{(x+\log (x)+\log (x) \log (5+x))^3}-\frac {5}{x (x+\log (x)+\log (x) \log (5+x))^3}+\frac {1}{\log (x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {5}{x \log (x) (x+\log (x)+\log (x) \log (5+x))^3}-\frac {\log (x)}{x (x+\log (x)+\log (x) \log (5+x))^3}\right ) \, dx+\frac {2}{25} \int \left (\frac {5}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {x}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3}-\frac {5}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3}-\frac {x}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {\log (x)}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3}\right ) \, dx+\frac {2}{5} \int \left (\frac {5}{x^2 (x+\log (x)+\log (x) \log (5+x))^3}+\frac {1}{x (x+\log (x)+\log (x) \log (5+x))^3}-\frac {5}{x^2 \log (x) (x+\log (x)+\log (x) \log (5+x))^3}-\frac {1}{x \log (x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {\log (x)}{x^2 (x+\log (x)+\log (x) \log (5+x))^3}\right ) \, dx+2 \int \frac {1}{x^3 (x+\log (x)+\log (x) \log (5+x))^2} \, dx+2 \int \frac {1}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2} \, dx\\ &=\log (x)-\frac {2}{25} \int \frac {1}{(x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {x}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {1}{\log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx-\frac {2}{25} \int \frac {x}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx-\frac {2}{25} \int \frac {\log (x)}{x (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {\log (x)}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{5} \int \frac {1}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx-\frac {2}{5} \int \frac {1}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{5} \int \frac {\log (x)}{x^2 (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^2 (x+\log (x)+\log (x) \log (5+x))^3} \, dx-2 \int \frac {1}{x^2 \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^3 (x+\log (x)+\log (x) \log (5+x))^2} \, dx+2 \int \frac {1}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2} \, dx\\ &=\log (x)-\frac {2}{25} \int \frac {1}{(x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {1}{\log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx-\frac {2}{25} \int \frac {\log (x)}{x (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {\log (x)}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \left (\frac {1}{(x+\log (x)+\log (x) \log (5+x))^3}-\frac {5}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3}\right ) \, dx-\frac {2}{25} \int \left (\frac {1}{\log (x) (x+\log (x)+\log (x) \log (5+x))^3}-\frac {5}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3}\right ) \, dx+\frac {2}{5} \int \frac {1}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx-\frac {2}{5} \int \frac {1}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{5} \int \frac {\log (x)}{x^2 (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^2 (x+\log (x)+\log (x) \log (5+x))^3} \, dx-2 \int \frac {1}{x^2 \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^3 (x+\log (x)+\log (x) \log (5+x))^2} \, dx+2 \int \frac {1}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2} \, dx\\ &=\log (x)-\frac {2}{25} \int \frac {\log (x)}{x (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {\log (x)}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{5} \int \frac {\log (x)}{x^2 (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^2 (x+\log (x)+\log (x) \log (5+x))^3} \, dx-2 \int \frac {1}{x^2 \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^3 (x+\log (x)+\log (x) \log (5+x))^2} \, dx+2 \int \frac {1}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.14, size = 21, normalized size = 0.95 \begin {gather*} \log (x)-\frac {1}{x^2 (x+\log (x)+\log (x) \log (5+x))^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(10 + 22*x + 4*x^2 + 5*x^5 + x^6 + (10 + 4*x + 15*x^4 + 3*x^5)*Log[x] + (15*x^3 + 3*x^4)*Log[x]^2 +
(5*x^2 + x^3)*Log[x]^3 + (10 + 2*x + (10 + 2*x + 15*x^4 + 3*x^5)*Log[x] + (30*x^3 + 6*x^4)*Log[x]^2 + (15*x^2
+ 3*x^3)*Log[x]^3)*Log[5 + x] + ((15*x^3 + 3*x^4)*Log[x]^2 + (15*x^2 + 3*x^3)*Log[x]^3)*Log[5 + x]^2 + (5*x^2
+ x^3)*Log[x]^3*Log[5 + x]^3)/(5*x^6 + x^7 + (15*x^5 + 3*x^6)*Log[x] + (15*x^4 + 3*x^5)*Log[x]^2 + (5*x^3 + x^
4)*Log[x]^3 + ((15*x^5 + 3*x^6)*Log[x] + (30*x^4 + 6*x^5)*Log[x]^2 + (15*x^3 + 3*x^4)*Log[x]^3)*Log[5 + x] + (
(15*x^4 + 3*x^5)*Log[x]^2 + (15*x^3 + 3*x^4)*Log[x]^3)*Log[5 + x]^2 + (5*x^3 + x^4)*Log[x]^3*Log[5 + x]^3),x]

[Out]

Log[x] - 1/(x^2*(x + Log[x] + Log[x]*Log[5 + x])^2)

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fricas [B]  time = 0.77, size = 119, normalized size = 5.41 \begin {gather*} \frac {x^{2} \log \left (x + 5\right )^{2} \log \relax (x)^{3} + x^{4} \log \relax (x) + 2 \, x^{3} \log \relax (x)^{2} + x^{2} \log \relax (x)^{3} + 2 \, {\left (x^{3} \log \relax (x)^{2} + x^{2} \log \relax (x)^{3}\right )} \log \left (x + 5\right ) - 1}{x^{2} \log \left (x + 5\right )^{2} \log \relax (x)^{2} + x^{4} + 2 \, x^{3} \log \relax (x) + x^{2} \log \relax (x)^{2} + 2 \, {\left (x^{3} \log \relax (x) + x^{2} \log \relax (x)^{2}\right )} \log \left (x + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^3+5*x^2)*log(x)^3*log(5+x)^3+((3*x^3+15*x^2)*log(x)^3+(3*x^4+15*x^3)*log(x)^2)*log(5+x)^2+((3*x^
3+15*x^2)*log(x)^3+(6*x^4+30*x^3)*log(x)^2+(3*x^5+15*x^4+2*x+10)*log(x)+2*x+10)*log(5+x)+(x^3+5*x^2)*log(x)^3+
(3*x^4+15*x^3)*log(x)^2+(3*x^5+15*x^4+4*x+10)*log(x)+x^6+5*x^5+4*x^2+22*x+10)/((x^4+5*x^3)*log(x)^3*log(5+x)^3
+((3*x^4+15*x^3)*log(x)^3+(3*x^5+15*x^4)*log(x)^2)*log(5+x)^2+((3*x^4+15*x^3)*log(x)^3+(6*x^5+30*x^4)*log(x)^2
+(3*x^6+15*x^5)*log(x))*log(5+x)+(x^4+5*x^3)*log(x)^3+(3*x^5+15*x^4)*log(x)^2+(3*x^6+15*x^5)*log(x)+x^7+5*x^6)
,x, algorithm="fricas")

[Out]

(x^2*log(x + 5)^2*log(x)^3 + x^4*log(x) + 2*x^3*log(x)^2 + x^2*log(x)^3 + 2*(x^3*log(x)^2 + x^2*log(x)^3)*log(
x + 5) - 1)/(x^2*log(x + 5)^2*log(x)^2 + x^4 + 2*x^3*log(x) + x^2*log(x)^2 + 2*(x^3*log(x) + x^2*log(x)^2)*log
(x + 5))

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giac [B]  time = 0.64, size = 281, normalized size = 12.77 \begin {gather*} -\frac {x \log \relax (x) + \log \relax (x)^{2} - x + 5 \, \log \relax (x) - 5}{x^{3} \log \left (x + 5\right )^{2} \log \relax (x)^{3} + x^{2} \log \left (x + 5\right )^{2} \log \relax (x)^{4} + 2 \, x^{4} \log \left (x + 5\right ) \log \relax (x)^{2} - x^{3} \log \left (x + 5\right )^{2} \log \relax (x)^{2} + 4 \, x^{3} \log \left (x + 5\right ) \log \relax (x)^{3} + 5 \, x^{2} \log \left (x + 5\right )^{2} \log \relax (x)^{3} + 2 \, x^{2} \log \left (x + 5\right ) \log \relax (x)^{4} + x^{5} \log \relax (x) - 2 \, x^{4} \log \left (x + 5\right ) \log \relax (x) + 3 \, x^{4} \log \relax (x)^{2} + 8 \, x^{3} \log \left (x + 5\right ) \log \relax (x)^{2} - 5 \, x^{2} \log \left (x + 5\right )^{2} \log \relax (x)^{2} + 3 \, x^{3} \log \relax (x)^{3} + 10 \, x^{2} \log \left (x + 5\right ) \log \relax (x)^{3} + x^{2} \log \relax (x)^{4} - x^{5} + 3 \, x^{4} \log \relax (x) - 10 \, x^{3} \log \left (x + 5\right ) \log \relax (x) + 9 \, x^{3} \log \relax (x)^{2} - 10 \, x^{2} \log \left (x + 5\right ) \log \relax (x)^{2} + 5 \, x^{2} \log \relax (x)^{3} - 5 \, x^{4} - 10 \, x^{3} \log \relax (x) - 5 \, x^{2} \log \relax (x)^{2}} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^3+5*x^2)*log(x)^3*log(5+x)^3+((3*x^3+15*x^2)*log(x)^3+(3*x^4+15*x^3)*log(x)^2)*log(5+x)^2+((3*x^
3+15*x^2)*log(x)^3+(6*x^4+30*x^3)*log(x)^2+(3*x^5+15*x^4+2*x+10)*log(x)+2*x+10)*log(5+x)+(x^3+5*x^2)*log(x)^3+
(3*x^4+15*x^3)*log(x)^2+(3*x^5+15*x^4+4*x+10)*log(x)+x^6+5*x^5+4*x^2+22*x+10)/((x^4+5*x^3)*log(x)^3*log(5+x)^3
+((3*x^4+15*x^3)*log(x)^3+(3*x^5+15*x^4)*log(x)^2)*log(5+x)^2+((3*x^4+15*x^3)*log(x)^3+(6*x^5+30*x^4)*log(x)^2
+(3*x^6+15*x^5)*log(x))*log(5+x)+(x^4+5*x^3)*log(x)^3+(3*x^5+15*x^4)*log(x)^2+(3*x^6+15*x^5)*log(x)+x^7+5*x^6)
,x, algorithm="giac")

[Out]

-(x*log(x) + log(x)^2 - x + 5*log(x) - 5)/(x^3*log(x + 5)^2*log(x)^3 + x^2*log(x + 5)^2*log(x)^4 + 2*x^4*log(x
+ 5)*log(x)^2 - x^3*log(x + 5)^2*log(x)^2 + 4*x^3*log(x + 5)*log(x)^3 + 5*x^2*log(x + 5)^2*log(x)^3 + 2*x^2*l
og(x + 5)*log(x)^4 + x^5*log(x) - 2*x^4*log(x + 5)*log(x) + 3*x^4*log(x)^2 + 8*x^3*log(x + 5)*log(x)^2 - 5*x^2
*log(x + 5)^2*log(x)^2 + 3*x^3*log(x)^3 + 10*x^2*log(x + 5)*log(x)^3 + x^2*log(x)^4 - x^5 + 3*x^4*log(x) - 10*
x^3*log(x + 5)*log(x) + 9*x^3*log(x)^2 - 10*x^2*log(x + 5)*log(x)^2 + 5*x^2*log(x)^3 - 5*x^4 - 10*x^3*log(x) -
5*x^2*log(x)^2) + log(x)

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maple [A]  time = 0.05, size = 22, normalized size = 1.00

method	result	size
risch	\(\ln \relax (x )-\frac {1}{x^{2} \left (\ln \relax (x ) \ln \left (5+x \right )+\ln \relax (x )+x \right )^{2}}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x^3+5*x^2)*ln(x)^3*ln(5+x)^3+((3*x^3+15*x^2)*ln(x)^3+(3*x^4+15*x^3)*ln(x)^2)*ln(5+x)^2+((3*x^3+15*x^2)*l
n(x)^3+(6*x^4+30*x^3)*ln(x)^2+(3*x^5+15*x^4+2*x+10)*ln(x)+2*x+10)*ln(5+x)+(x^3+5*x^2)*ln(x)^3+(3*x^4+15*x^3)*l
n(x)^2+(3*x^5+15*x^4+4*x+10)*ln(x)+x^6+5*x^5+4*x^2+22*x+10)/((x^4+5*x^3)*ln(x)^3*ln(5+x)^3+((3*x^4+15*x^3)*ln(
x)^3+(3*x^5+15*x^4)*ln(x)^2)*ln(5+x)^2+((3*x^4+15*x^3)*ln(x)^3+(6*x^5+30*x^4)*ln(x)^2+(3*x^6+15*x^5)*ln(x))*ln
(5+x)+(x^4+5*x^3)*ln(x)^3+(3*x^5+15*x^4)*ln(x)^2+(3*x^6+15*x^5)*ln(x)+x^7+5*x^6),x,method=_RETURNVERBOSE)

[Out]

ln(x)-1/x^2/(ln(x)*ln(5+x)+ln(x)+x)^2

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maxima [B]  time = 0.47, size = 61, normalized size = 2.77 \begin {gather*} -\frac {1}{x^{2} \log \left (x + 5\right )^{2} \log \relax (x)^{2} + x^{4} + 2 \, x^{3} \log \relax (x) + x^{2} \log \relax (x)^{2} + 2 \, {\left (x^{3} \log \relax (x) + x^{2} \log \relax (x)^{2}\right )} \log \left (x + 5\right )} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^3+5*x^2)*log(x)^3*log(5+x)^3+((3*x^3+15*x^2)*log(x)^3+(3*x^4+15*x^3)*log(x)^2)*log(5+x)^2+((3*x^
3+15*x^2)*log(x)^3+(6*x^4+30*x^3)*log(x)^2+(3*x^5+15*x^4+2*x+10)*log(x)+2*x+10)*log(5+x)+(x^3+5*x^2)*log(x)^3+
(3*x^4+15*x^3)*log(x)^2+(3*x^5+15*x^4+4*x+10)*log(x)+x^6+5*x^5+4*x^2+22*x+10)/((x^4+5*x^3)*log(x)^3*log(5+x)^3
+((3*x^4+15*x^3)*log(x)^3+(3*x^5+15*x^4)*log(x)^2)*log(5+x)^2+((3*x^4+15*x^3)*log(x)^3+(6*x^5+30*x^4)*log(x)^2
+(3*x^6+15*x^5)*log(x))*log(5+x)+(x^4+5*x^3)*log(x)^3+(3*x^5+15*x^4)*log(x)^2+(3*x^6+15*x^5)*log(x)+x^7+5*x^6)
,x, algorithm="maxima")

[Out]

-1/(x^2*log(x + 5)^2*log(x)^2 + x^4 + 2*x^3*log(x) + x^2*log(x)^2 + 2*(x^3*log(x) + x^2*log(x)^2)*log(x + 5))
+ log(x)

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mupad [B]  time = 6.09, size = 82, normalized size = 3.73 \begin {gather*} \frac {x^4\,\ln \relax (x)+2\,x^3\,\ln \left (x+5\right )\,{\ln \relax (x)}^2+2\,x^3\,{\ln \relax (x)}^2+x^2\,{\ln \left (x+5\right )}^2\,{\ln \relax (x)}^3+2\,x^2\,\ln \left (x+5\right )\,{\ln \relax (x)}^3+x^2\,{\ln \relax (x)}^3-1}{x^2\,{\left (x+\ln \relax (x)+\ln \left (x+5\right )\,\ln \relax (x)\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((22*x + log(x)^3*(5*x^2 + x^3) + log(x + 5)^2*(log(x)^3*(15*x^2 + 3*x^3) + log(x)^2*(15*x^3 + 3*x^4)) + lo
g(x)^2*(15*x^3 + 3*x^4) + log(x + 5)*(2*x + log(x)^3*(15*x^2 + 3*x^3) + log(x)^2*(30*x^3 + 6*x^4) + log(x)*(2*
x + 15*x^4 + 3*x^5 + 10) + 10) + 4*x^2 + 5*x^5 + x^6 + log(x)*(4*x + 15*x^4 + 3*x^5 + 10) + log(x + 5)^3*log(x
)^3*(5*x^2 + x^3) + 10)/(log(x)*(15*x^5 + 3*x^6) + log(x)^3*(5*x^3 + x^4) + log(x + 5)^2*(log(x)^3*(15*x^3 + 3
*x^4) + log(x)^2*(15*x^4 + 3*x^5)) + log(x)^2*(15*x^4 + 3*x^5) + 5*x^6 + x^7 + log(x + 5)*(log(x)*(15*x^5 + 3*
x^6) + log(x)^3*(15*x^3 + 3*x^4) + log(x)^2*(30*x^4 + 6*x^5)) + log(x + 5)^3*log(x)^3*(5*x^3 + x^4)),x)

[Out]

(x^4*log(x) + x^2*log(x)^3 + 2*x^3*log(x)^2 + x^2*log(x + 5)^2*log(x)^3 + 2*x^2*log(x + 5)*log(x)^3 + 2*x^3*lo
g(x + 5)*log(x)^2 - 1)/(x^2*(x + log(x) + log(x + 5)*log(x))^2)

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sympy [B]  time = 0.52, size = 63, normalized size = 2.86 \begin {gather*} \log {\relax (x )} - \frac {1}{x^{4} + 2 x^{3} \log {\relax (x )} + x^{2} \log {\relax (x )}^{2} \log {\left (x + 5 \right )}^{2} + x^{2} \log {\relax (x )}^{2} + \left (2 x^{3} \log {\relax (x )} + 2 x^{2} \log {\relax (x )}^{2}\right ) \log {\left (x + 5 \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x**3+5*x**2)*ln(x)**3*ln(5+x)**3+((3*x**3+15*x**2)*ln(x)**3+(3*x**4+15*x**3)*ln(x)**2)*ln(5+x)**2+
((3*x**3+15*x**2)*ln(x)**3+(6*x**4+30*x**3)*ln(x)**2+(3*x**5+15*x**4+2*x+10)*ln(x)+2*x+10)*ln(5+x)+(x**3+5*x**
2)*ln(x)**3+(3*x**4+15*x**3)*ln(x)**2+(3*x**5+15*x**4+4*x+10)*ln(x)+x**6+5*x**5+4*x**2+22*x+10)/((x**4+5*x**3)
*ln(x)**3*ln(5+x)**3+((3*x**4+15*x**3)*ln(x)**3+(3*x**5+15*x**4)*ln(x)**2)*ln(5+x)**2+((3*x**4+15*x**3)*ln(x)*
*3+(6*x**5+30*x**4)*ln(x)**2+(3*x**6+15*x**5)*ln(x))*ln(5+x)+(x**4+5*x**3)*ln(x)**3+(3*x**5+15*x**4)*ln(x)**2+
(3*x**6+15*x**5)*ln(x)+x**7+5*x**6),x)

[Out]

log(x) - 1/(x**4 + 2*x**3*log(x) + x**2*log(x)**2*log(x + 5)**2 + x**2*log(x)**2 + (2*x**3*log(x) + 2*x**2*log
(x)**2)*log(x + 5))

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