\(\int \frac {50+50 x+(51+103 x+2 x^2) \log (x)+(1250+1250 x+(1300+2550 x) \log (x)) \log (1+x)+(625+625 x) \log (x) \log ^2(1+x)+(1250+1250 x+(1300+2550 x) \log (x)+(1250+1250 x) \log (x) \log (1+x)) \log (4 x \log (x))+(625+625 x) \log (x) \log ^2(4 x \log (x))}{(1+x) \log (x)} \, dx\) [8747]

Optimal result

Integrand size = 108, antiderivative size = 21 \[ \int \frac {50+50 x+\left (51+103 x+2 x^2\right ) \log (x)+(1250+1250 x+(1300+2550 x) \log (x)) \log (1+x)+(625+625 x) \log (x) \log ^2(1+x)+(1250+1250 x+(1300+2550 x) \log (x)+(1250+1250 x) \log (x) \log (1+x)) \log (4 x \log (x))+(625+625 x) \log (x) \log ^2(4 x \log (x))}{(1+x) \log (x)} \, dx=x \left (x+(1+25 (\log (1+x)+\log (4 x \log (x))))^2\right ) \]

[Out]

(x+(25*ln(1+x)+25*ln(4*x*ln(x))+1)^2)*x

Rubi [F]

\[ \int \frac {50+50 x+\left (51+103 x+2 x^2\right ) \log (x)+(1250+1250 x+(1300+2550 x) \log (x)) \log (1+x)+(625+625 x) \log (x) \log ^2(1+x)+(1250+1250 x+(1300+2550 x) \log (x)+(1250+1250 x) \log (x) \log (1+x)) \log (4 x \log (x))+(625+625 x) \log (x) \log ^2(4 x \log (x))}{(1+x) \log (x)} \, dx=\int \frac {50+50 x+\left (51+103 x+2 x^2\right ) \log (x)+(1250+1250 x+(1300+2550 x) \log (x)) \log (1+x)+(625+625 x) \log (x) \log ^2(1+x)+(1250+1250 x+(1300+2550 x) \log (x)+(1250+1250 x) \log (x) \log (1+x)) \log (4 x \log (x))+(625+625 x) \log (x) \log ^2(4 x \log (x))}{(1+x) \log (x)} \, dx \]

[In]

Int[(50 + 50*x + (51 + 103*x + 2*x^2)*Log[x] + (1250 + 1250*x + (1300 + 2550*x)*Log[x])*Log[1 + x] + (625 + 62
5*x)*Log[x]*Log[1 + x]^2 + (1250 + 1250*x + (1300 + 2550*x)*Log[x] + (1250 + 1250*x)*Log[x]*Log[1 + x])*Log[4*
x*Log[x]] + (625 + 625*x)*Log[x]*Log[4*x*Log[x]]^2)/((1 + x)*Log[x]),x]

[Out]

-2499*x + x^2 - 50*Log[1 + x] + 1300*(1 + x)*Log[1 + x] - 625*Log[1 + x]^2 + 625*(1 + x)*Log[1 + x]^2 + 2550*x
*Log[4*x*Log[x]] - 2550*LogIntegral[x] - 1250*Log[x]*LogIntegral[x] + 1250*Log[4*x*Log[x]]*LogIntegral[x] + 50
*Defer[Int][(1 + 25*Log[1 + x])/Log[x], x] - 1250*Defer[Int][Log[4*x*Log[x]]/(1 + x), x] + 1250*Defer[Int][Log
[1 + x]*Log[4*x*Log[x]], x] + 625*Defer[Int][Log[4*x*Log[x]]^2, x] - 1250*Defer[Int][LogIntegral[x]/(x*Log[x])
, x]

Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {50+50 x+51 \log (x)+103 x \log (x)+2 x^2 \log (x)+1250 \log (1+x)+1250 x \log (1+x)+1300 \log (x) \log (1+x)+2550 x \log (x) \log (1+x)+625 \log (x) \log ^2(1+x)+625 x \log (x) \log ^2(1+x)}{(1+x) \log (x)}+\frac {50 (25+25 x+26 \log (x)+51 x \log (x)+25 \log (x) \log (1+x)+25 x \log (x) \log (1+x)) \log (4 x \log (x))}{(1+x) \log (x)}+625 \log ^2(4 x \log (x))\right ) \, dx \\ & = 50 \int \frac {(25+25 x+26 \log (x)+51 x \log (x)+25 \log (x) \log (1+x)+25 x \log (x) \log (1+x)) \log (4 x \log (x))}{(1+x) \log (x)} \, dx+625 \int \log ^2(4 x \log (x)) \, dx+\int \frac {50+50 x+51 \log (x)+103 x \log (x)+2 x^2 \log (x)+1250 \log (1+x)+1250 x \log (1+x)+1300 \log (x) \log (1+x)+2550 x \log (x) \log (1+x)+625 \log (x) \log ^2(1+x)+625 x \log (x) \log ^2(1+x)}{(1+x) \log (x)} \, dx \\ & = 50 \int \frac {(25 (1+x)+\log (x) (26+51 x+25 (1+x) \log (1+x))) \log (4 x \log (x))}{(1+x) \log (x)} \, dx+625 \int \log ^2(4 x \log (x)) \, dx+\int \left (\frac {50 (1+25 \log (1+x))}{\log (x)}+\frac {51+103 x+2 x^2+50 (26+51 x) \log (1+x)+625 (1+x) \log ^2(1+x)}{1+x}\right ) \, dx \\ & = 50 \int \frac {1+25 \log (1+x)}{\log (x)} \, dx+50 \int \left (\frac {26 \log (4 x \log (x))}{1+x}+\frac {51 x \log (4 x \log (x))}{1+x}+\frac {25 \log (4 x \log (x))}{(1+x) \log (x)}+\frac {25 x \log (4 x \log (x))}{(1+x) \log (x)}+\frac {25 \log (1+x) \log (4 x \log (x))}{1+x}+\frac {25 x \log (1+x) \log (4 x \log (x))}{1+x}\right ) \, dx+625 \int \log ^2(4 x \log (x)) \, dx+\int \frac {51+103 x+2 x^2+50 (26+51 x) \log (1+x)+625 (1+x) \log ^2(1+x)}{1+x} \, dx \\ & = 50 \int \frac {1+25 \log (1+x)}{\log (x)} \, dx+625 \int \log ^2(4 x \log (x)) \, dx+1250 \int \frac {\log (4 x \log (x))}{(1+x) \log (x)} \, dx+1250 \int \frac {x \log (4 x \log (x))}{(1+x) \log (x)} \, dx+1250 \int \frac {\log (1+x) \log (4 x \log (x))}{1+x} \, dx+1250 \int \frac {x \log (1+x) \log (4 x \log (x))}{1+x} \, dx+1300 \int \frac {\log (4 x \log (x))}{1+x} \, dx+2550 \int \frac {x \log (4 x \log (x))}{1+x} \, dx+\int \left (\frac {51+103 x+2 x^2}{1+x}+\frac {50 (26+51 x) \log (1+x)}{1+x}+625 \log ^2(1+x)\right ) \, dx \\ & = 50 \int \frac {(26+51 x) \log (1+x)}{1+x} \, dx+50 \int \frac {1+25 \log (1+x)}{\log (x)} \, dx+625 \int \log ^2(1+x) \, dx+625 \int \log ^2(4 x \log (x)) \, dx+1250 \int \frac {\log (4 x \log (x))}{(1+x) \log (x)} \, dx+1250 \int \frac {\log (1+x) \log (4 x \log (x))}{1+x} \, dx+1250 \int \left (\frac {\log (4 x \log (x))}{\log (x)}-\frac {\log (4 x \log (x))}{(1+x) \log (x)}\right ) \, dx+1250 \int \left (\log (1+x) \log (4 x \log (x))-\frac {\log (1+x) \log (4 x \log (x))}{1+x}\right ) \, dx+1300 \int \frac {\log (4 x \log (x))}{1+x} \, dx+2550 \int \left (\log (4 x \log (x))-\frac {\log (4 x \log (x))}{1+x}\right ) \, dx+\int \frac {51+103 x+2 x^2}{1+x} \, dx \\ & = 50 \int \frac {1+25 \log (1+x)}{\log (x)} \, dx+50 \text {Subst}\left (\int \frac {(-25+51 x) \log (x)}{x} \, dx,x,1+x\right )+625 \int \log ^2(4 x \log (x)) \, dx+625 \text {Subst}\left (\int \log ^2(x) \, dx,x,1+x\right )+1250 \int \frac {\log (4 x \log (x))}{\log (x)} \, dx+1250 \int \log (1+x) \log (4 x \log (x)) \, dx+1300 \int \frac {\log (4 x \log (x))}{1+x} \, dx+2550 \int \log (4 x \log (x)) \, dx-2550 \int \frac {\log (4 x \log (x))}{1+x} \, dx+\int \left (101+2 x-\frac {50}{1+x}\right ) \, dx \\ & = 101 x+x^2-50 \log (1+x)+625 (1+x) \log ^2(1+x)+2550 x \log (4 x \log (x))+1250 \log (4 x \log (x)) \operatorname {LogIntegral}(x)+50 \int \frac {1+25 \log (1+x)}{\log (x)} \, dx+625 \int \log ^2(4 x \log (x)) \, dx+1250 \int \log (1+x) \log (4 x \log (x)) \, dx-1250 \int \frac {(1+\log (x)) \operatorname {LogIntegral}(x)}{x \log (x)} \, dx-1250 \text {Subst}(\int \log (x) \, dx,x,1+x)-1250 \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,1+x\right )+1300 \int \frac {\log (4 x \log (x))}{1+x} \, dx-2550 \int \left (1+\frac {1}{\log (x)}\right ) \, dx-2550 \int \frac {\log (4 x \log (x))}{1+x} \, dx+2550 \text {Subst}(\int \log (x) \, dx,x,1+x) \\ & = -3749 x+x^2-50 \log (1+x)+1300 (1+x) \log (1+x)-625 \log ^2(1+x)+625 (1+x) \log ^2(1+x)+2550 x \log (4 x \log (x))+1250 \log (4 x \log (x)) \operatorname {LogIntegral}(x)+50 \int \frac {1+25 \log (1+x)}{\log (x)} \, dx+625 \int \log ^2(4 x \log (x)) \, dx+1250 \int \log (1+x) \log (4 x \log (x)) \, dx-1250 \int \left (\frac {\operatorname {LogIntegral}(x)}{x}+\frac {\operatorname {LogIntegral}(x)}{x \log (x)}\right ) \, dx+1300 \int \frac {\log (4 x \log (x))}{1+x} \, dx-2550 \int \frac {1}{\log (x)} \, dx-2550 \int \frac {\log (4 x \log (x))}{1+x} \, dx \\ & = -3749 x+x^2-50 \log (1+x)+1300 (1+x) \log (1+x)-625 \log ^2(1+x)+625 (1+x) \log ^2(1+x)+2550 x \log (4 x \log (x))-2550 \operatorname {LogIntegral}(x)+1250 \log (4 x \log (x)) \operatorname {LogIntegral}(x)+50 \int \frac {1+25 \log (1+x)}{\log (x)} \, dx+625 \int \log ^2(4 x \log (x)) \, dx+1250 \int \log (1+x) \log (4 x \log (x)) \, dx-1250 \int \frac {\operatorname {LogIntegral}(x)}{x} \, dx-1250 \int \frac {\operatorname {LogIntegral}(x)}{x \log (x)} \, dx+1300 \int \frac {\log (4 x \log (x))}{1+x} \, dx-2550 \int \frac {\log (4 x \log (x))}{1+x} \, dx \\ & = -2499 x+x^2-50 \log (1+x)+1300 (1+x) \log (1+x)-625 \log ^2(1+x)+625 (1+x) \log ^2(1+x)+2550 x \log (4 x \log (x))-2550 \operatorname {LogIntegral}(x)-1250 \log (x) \operatorname {LogIntegral}(x)+1250 \log (4 x \log (x)) \operatorname {LogIntegral}(x)+50 \int \frac {1+25 \log (1+x)}{\log (x)} \, dx+625 \int \log ^2(4 x \log (x)) \, dx+1250 \int \log (1+x) \log (4 x \log (x)) \, dx-1250 \int \frac {\operatorname {LogIntegral}(x)}{x \log (x)} \, dx+1300 \int \frac {\log (4 x \log (x))}{1+x} \, dx-2550 \int \frac {\log (4 x \log (x))}{1+x} \, dx \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(45\) vs. \(2(21)=42\).

Time = 0.18 (sec) , antiderivative size = 45, normalized size of antiderivative = 2.14 \[ \int \frac {50+50 x+\left (51+103 x+2 x^2\right ) \log (x)+(1250+1250 x+(1300+2550 x) \log (x)) \log (1+x)+(625+625 x) \log (x) \log ^2(1+x)+(1250+1250 x+(1300+2550 x) \log (x)+(1250+1250 x) \log (x) \log (1+x)) \log (4 x \log (x))+(625+625 x) \log (x) \log ^2(4 x \log (x))}{(1+x) \log (x)} \, dx=x \left (1+x+50 \log (1+x)+625 \log ^2(1+x)+50 (1+25 \log (1+x)) \log (4 x \log (x))+625 \log ^2(4 x \log (x))\right ) \]

[In]

Integrate[(50 + 50*x + (51 + 103*x + 2*x^2)*Log[x] + (1250 + 1250*x + (1300 + 2550*x)*Log[x])*Log[1 + x] + (62
5 + 625*x)*Log[x]*Log[1 + x]^2 + (1250 + 1250*x + (1300 + 2550*x)*Log[x] + (1250 + 1250*x)*Log[x]*Log[1 + x])*
Log[4*x*Log[x]] + (625 + 625*x)*Log[x]*Log[4*x*Log[x]]^2)/((1 + x)*Log[x]),x]

[Out]

x*(1 + x + 50*Log[1 + x] + 625*Log[1 + x]^2 + 50*(1 + 25*Log[1 + x])*Log[4*x*Log[x]] + 625*Log[4*x*Log[x]]^2)

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(55\) vs. \(2(22)=44\).

Time = 1.73 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.67

method	result	size
parallelrisch	\(625 x \ln \left (1+x \right )^{2}+1250 \ln \left (4 x \ln \left (x \right )\right ) \ln \left (1+x \right ) x +625 \ln \left (4 x \ln \left (x \right )\right )^{2} x -\frac {1}{2}+x^{2}+50 \ln \left (1+x \right ) x +50 \ln \left (4 x \ln \left (x \right )\right ) x +x\)	\(56\)
risch	\(\text {Expression too large to display}\)	\(729\)

[In]

int(((625*x+625)*ln(x)*ln(4*x*ln(x))^2+((1250*x+1250)*ln(x)*ln(1+x)+(2550*x+1300)*ln(x)+1250*x+1250)*ln(4*x*ln
(x))+(625*x+625)*ln(x)*ln(1+x)^2+((2550*x+1300)*ln(x)+1250*x+1250)*ln(1+x)+(2*x^2+103*x+51)*ln(x)+50*x+50)/ln(
x)/(1+x),x,method=_RETURNVERBOSE)

[Out]

625*x*ln(1+x)^2+1250*ln(4*x*ln(x))*ln(1+x)*x+625*ln(4*x*ln(x))^2*x-1/2+x^2+50*ln(1+x)*x+50*ln(4*x*ln(x))*x+x

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (22) = 44\).

Time = 0.28 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.33 \[ \int \frac {50+50 x+\left (51+103 x+2 x^2\right ) \log (x)+(1250+1250 x+(1300+2550 x) \log (x)) \log (1+x)+(625+625 x) \log (x) \log ^2(1+x)+(1250+1250 x+(1300+2550 x) \log (x)+(1250+1250 x) \log (x) \log (1+x)) \log (4 x \log (x))+(625+625 x) \log (x) \log ^2(4 x \log (x))}{(1+x) \log (x)} \, dx=625 \, x \log \left (4 \, x \log \left (x\right )\right )^{2} + 625 \, x \log \left (x + 1\right )^{2} + x^{2} + 50 \, {\left (25 \, x \log \left (x + 1\right ) + x\right )} \log \left (4 \, x \log \left (x\right )\right ) + 50 \, x \log \left (x + 1\right ) + x \]

[In]

integrate(((625*x+625)*log(x)*log(4*x*log(x))^2+((1250*x+1250)*log(x)*log(1+x)+(2550*x+1300)*log(x)+1250*x+125
0)*log(4*x*log(x))+(625*x+625)*log(x)*log(1+x)^2+((2550*x+1300)*log(x)+1250*x+1250)*log(1+x)+(2*x^2+103*x+51)*
log(x)+50*x+50)/log(x)/(1+x),x, algorithm="fricas")

[Out]

625*x*log(4*x*log(x))^2 + 625*x*log(x + 1)^2 + x^2 + 50*(25*x*log(x + 1) + x)*log(4*x*log(x)) + 50*x*log(x + 1
) + x

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (22) = 44\).

Time = 4.66 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.67 \[ \int \frac {50+50 x+\left (51+103 x+2 x^2\right ) \log (x)+(1250+1250 x+(1300+2550 x) \log (x)) \log (1+x)+(625+625 x) \log (x) \log ^2(1+x)+(1250+1250 x+(1300+2550 x) \log (x)+(1250+1250 x) \log (x) \log (1+x)) \log (4 x \log (x))+(625+625 x) \log (x) \log ^2(4 x \log (x))}{(1+x) \log (x)} \, dx=x^{2} + 625 x \log {\left (4 x \log {\left (x \right )} \right )}^{2} + 625 x \log {\left (x + 1 \right )}^{2} + 50 x \log {\left (x + 1 \right )} + x + \left (1250 x \log {\left (x + 1 \right )} + 50 x\right ) \log {\left (4 x \log {\left (x \right )} \right )} \]

[In]

integrate(((625*x+625)*ln(x)*ln(4*x*ln(x))**2+((1250*x+1250)*ln(x)*ln(1+x)+(2550*x+1300)*ln(x)+1250*x+1250)*ln
(4*x*ln(x))+(625*x+625)*ln(x)*ln(1+x)**2+((2550*x+1300)*ln(x)+1250*x+1250)*ln(1+x)+(2*x**2+103*x+51)*ln(x)+50*
x+50)/ln(x)/(1+x),x)

[Out]

x**2 + 625*x*log(4*x*log(x))**2 + 625*x*log(x + 1)**2 + 50*x*log(x + 1) + x + (1250*x*log(x + 1) + 50*x)*log(4
*x*log(x))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 98 vs. \(2 (22) = 44\).

Time = 0.31 (sec) , antiderivative size = 98, normalized size of antiderivative = 4.67 \[ \int \frac {50+50 x+\left (51+103 x+2 x^2\right ) \log (x)+(1250+1250 x+(1300+2550 x) \log (x)) \log (1+x)+(625+625 x) \log (x) \log ^2(1+x)+(1250+1250 x+(1300+2550 x) \log (x)+(1250+1250 x) \log (x) \log (1+x)) \log (4 x \log (x))+(625+625 x) \log (x) \log ^2(4 x \log (x))}{(1+x) \log (x)} \, dx=625 \, x \log \left (x + 1\right )^{2} + 50 \, x {\left (50 \, \log \left (2\right ) + 1\right )} \log \left (x\right ) + 625 \, x \log \left (x\right )^{2} + 625 \, x \log \left (\log \left (x\right )\right )^{2} + {\left (2500 \, \log \left (2\right )^{2} + 100 \, \log \left (2\right ) + 1\right )} x + x^{2} + 50 \, {\left (x {\left (50 \, \log \left (2\right ) + 1\right )} + 25 \, x \log \left (x\right ) + 25 \, x \log \left (\log \left (x\right )\right )\right )} \log \left (x + 1\right ) + 50 \, {\left (x {\left (50 \, \log \left (2\right ) + 1\right )} + 25 \, x \log \left (x\right )\right )} \log \left (\log \left (x\right )\right ) \]

[In]

integrate(((625*x+625)*log(x)*log(4*x*log(x))^2+((1250*x+1250)*log(x)*log(1+x)+(2550*x+1300)*log(x)+1250*x+125
0)*log(4*x*log(x))+(625*x+625)*log(x)*log(1+x)^2+((2550*x+1300)*log(x)+1250*x+1250)*log(1+x)+(2*x^2+103*x+51)*
log(x)+50*x+50)/log(x)/(1+x),x, algorithm="maxima")

[Out]

625*x*log(x + 1)^2 + 50*x*(50*log(2) + 1)*log(x) + 625*x*log(x)^2 + 625*x*log(log(x))^2 + (2500*log(2)^2 + 100
*log(2) + 1)*x + x^2 + 50*(x*(50*log(2) + 1) + 25*x*log(x) + 25*x*log(log(x)))*log(x + 1) + 50*(x*(50*log(2) +
1) + 25*x*log(x))*log(log(x))

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (22) = 44\).

Time = 0.32 (sec) , antiderivative size = 70, normalized size of antiderivative = 3.33 \[ \int \frac {50+50 x+\left (51+103 x+2 x^2\right ) \log (x)+(1250+1250 x+(1300+2550 x) \log (x)) \log (1+x)+(625+625 x) \log (x) \log ^2(1+x)+(1250+1250 x+(1300+2550 x) \log (x)+(1250+1250 x) \log (x) \log (1+x)) \log (4 x \log (x))+(625+625 x) \log (x) \log ^2(4 x \log (x))}{(1+x) \log (x)} \, dx=625 \, x \log \left (x + 1\right )^{2} + 625 \, x \log \left (x\right )^{2} + 625 \, x \log \left (4 \, \log \left (x\right )\right )^{2} + x^{2} + 50 \, {\left (25 \, x \log \left (x\right ) + x\right )} \log \left (x + 1\right ) + 50 \, x \log \left (x\right ) + 50 \, {\left (25 \, x \log \left (x + 1\right ) + 25 \, x \log \left (x\right ) + x\right )} \log \left (4 \, \log \left (x\right )\right ) + x \]

[In]

integrate(((625*x+625)*log(x)*log(4*x*log(x))^2+((1250*x+1250)*log(x)*log(1+x)+(2550*x+1300)*log(x)+1250*x+125
0)*log(4*x*log(x))+(625*x+625)*log(x)*log(1+x)^2+((2550*x+1300)*log(x)+1250*x+1250)*log(1+x)+(2*x^2+103*x+51)*
log(x)+50*x+50)/log(x)/(1+x),x, algorithm="giac")

[Out]

625*x*log(x + 1)^2 + 625*x*log(x)^2 + 625*x*log(4*log(x))^2 + x^2 + 50*(25*x*log(x) + x)*log(x + 1) + 50*x*log
(x) + 50*(25*x*log(x + 1) + 25*x*log(x) + x)*log(4*log(x)) + x

Mupad [B] (verification not implemented)

Time = 14.65 (sec) , antiderivative size = 127, normalized size of antiderivative = 6.05 \[ \int \frac {50+50 x+\left (51+103 x+2 x^2\right ) \log (x)+(1250+1250 x+(1300+2550 x) \log (x)) \log (1+x)+(625+625 x) \log (x) \log ^2(1+x)+(1250+1250 x+(1300+2550 x) \log (x)+(1250+1250 x) \log (x) \log (1+x)) \log (4 x \log (x))+(625+625 x) \log (x) \log ^2(4 x \log (x))}{(1+x) \log (x)} \, dx=x+\ln \left (4\,x\,\ln \left (x\right )\right )\,\left (\frac {\ln \left (x+1\right )\,\left (1250\,x^2+1250\,x\right )}{x+1}-\frac {1250\,x^4+2500\,x^3+1250\,x^2}{x\,{\left (x+1\right )}^2}+\frac {1300\,x^4+2600\,x^3+1300\,x^2}{x\,{\left (x+1\right )}^2}\right )+50\,x\,\ln \left (x+1\right )+625\,x\,{\ln \left (x+1\right )}^2+x^2+\frac {{\ln \left (4\,x\,\ln \left (x\right )\right )}^2\,\left (625\,x^3+625\,x^2\right )}{x\,\left (x+1\right )} \]

[In]

int((50*x + log(x + 1)*(1250*x + log(x)*(2550*x + 1300) + 1250) + log(x)*(103*x + 2*x^2 + 51) + log(4*x*log(x)
)*(1250*x + log(x)*(2550*x + 1300) + log(x + 1)*log(x)*(1250*x + 1250) + 1250) + log(4*x*log(x))^2*log(x)*(625
*x + 625) + log(x + 1)^2*log(x)*(625*x + 625) + 50)/(log(x)*(x + 1)),x)

[Out]

x + log(4*x*log(x))*((log(x + 1)*(1250*x + 1250*x^2))/(x + 1) - (1250*x^2 + 2500*x^3 + 1250*x^4)/(x*(x + 1)^2)
+ (1300*x^2 + 2600*x^3 + 1300*x^4)/(x*(x + 1)^2)) + 50*x*log(x + 1) + 625*x*log(x + 1)^2 + x^2 + (log(4*x*log
(x))^2*(625*x^2 + 625*x^3))/(x*(x + 1))