\(\int \frac {-36 x-72 x^2+72 x \log (x)}{196 x^2-196 x \log (x)+49 \log ^2(x)} \, dx\) [3269]

Optimal result

Integrand size = 34, antiderivative size = 15 \[ \int \frac {-36 x-72 x^2+72 x \log (x)}{196 x^2-196 x \log (x)+49 \log ^2(x)} \, dx=\frac {36 x^2}{49 (-2 x+\log (x))} \]

[Out]

36/49*x^2/(ln(x)-2*x)

Rubi [F]

\[ \int \frac {-36 x-72 x^2+72 x \log (x)}{196 x^2-196 x \log (x)+49 \log ^2(x)} \, dx=\int \frac {-36 x-72 x^2+72 x \log (x)}{196 x^2-196 x \log (x)+49 \log ^2(x)} \, dx \]

[In]

Int[(-36*x - 72*x^2 + 72*x*Log[x])/(196*x^2 - 196*x*Log[x] + 49*Log[x]^2),x]

[Out]

(-36*Defer[Int][x/(2*x - Log[x])^2, x])/49 + (72*Defer[Int][x^2/(2*x - Log[x])^2, x])/49 - (72*Defer[Int][x/(2
*x - Log[x]), x])/49

Rubi steps \begin{align*} \text {integral}& = \int \frac {36 x (-1-2 x+2 \log (x))}{49 (2 x-\log (x))^2} \, dx \\ & = \frac {36}{49} \int \frac {x (-1-2 x+2 \log (x))}{(2 x-\log (x))^2} \, dx \\ & = \frac {36}{49} \int \left (\frac {x (-1+2 x)}{(2 x-\log (x))^2}-\frac {2 x}{2 x-\log (x)}\right ) \, dx \\ & = \frac {36}{49} \int \frac {x (-1+2 x)}{(2 x-\log (x))^2} \, dx-\frac {72}{49} \int \frac {x}{2 x-\log (x)} \, dx \\ & = \frac {36}{49} \int \left (-\frac {x}{(2 x-\log (x))^2}+\frac {2 x^2}{(2 x-\log (x))^2}\right ) \, dx-\frac {72}{49} \int \frac {x}{2 x-\log (x)} \, dx \\ & = -\left (\frac {36}{49} \int \frac {x}{(2 x-\log (x))^2} \, dx\right )+\frac {72}{49} \int \frac {x^2}{(2 x-\log (x))^2} \, dx-\frac {72}{49} \int \frac {x}{2 x-\log (x)} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.09 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {-36 x-72 x^2+72 x \log (x)}{196 x^2-196 x \log (x)+49 \log ^2(x)} \, dx=\frac {36 x^2}{49 (-2 x+\log (x))} \]

[In]

Integrate[(-36*x - 72*x^2 + 72*x*Log[x])/(196*x^2 - 196*x*Log[x] + 49*Log[x]^2),x]

[Out]

(36*x^2)/(49*(-2*x + Log[x]))

Maple [A] (verified)

Time = 1.71 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93

method	result	size
default	\(\frac {36 x^{2}}{49 \left (\ln \left (x \right )-2 x \right )}\)	\(14\)
norman	\(-\frac {36 x^{2}}{49 \left (2 x -\ln \left (x \right )\right )}\)	\(16\)
risch	\(-\frac {36 x^{2}}{49 \left (2 x -\ln \left (x \right )\right )}\)	\(16\)
parallelrisch	\(-\frac {36 x^{2}}{49 \left (2 x -\ln \left (x \right )\right )}\)	\(16\)

[In]

int((72*x*ln(x)-72*x^2-36*x)/(49*ln(x)^2-196*x*ln(x)+196*x^2),x,method=_RETURNVERBOSE)

[Out]

36/49*x^2/(ln(x)-2*x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {-36 x-72 x^2+72 x \log (x)}{196 x^2-196 x \log (x)+49 \log ^2(x)} \, dx=-\frac {36 \, x^{2}}{49 \, {\left (2 \, x - \log \left (x\right )\right )}} \]

[In]

integrate((72*x*log(x)-72*x^2-36*x)/(49*log(x)^2-196*x*log(x)+196*x^2),x, algorithm="fricas")

[Out]

-36/49*x^2/(2*x - log(x))

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \frac {-36 x-72 x^2+72 x \log (x)}{196 x^2-196 x \log (x)+49 \log ^2(x)} \, dx=\frac {36 x^{2}}{- 98 x + 49 \log {\left (x \right )}} \]

[In]

integrate((72*x*ln(x)-72*x**2-36*x)/(49*ln(x)**2-196*x*ln(x)+196*x**2),x)

[Out]

36*x**2/(-98*x + 49*log(x))

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {-36 x-72 x^2+72 x \log (x)}{196 x^2-196 x \log (x)+49 \log ^2(x)} \, dx=-\frac {36 \, x^{2}}{49 \, {\left (2 \, x - \log \left (x\right )\right )}} \]

[In]

integrate((72*x*log(x)-72*x^2-36*x)/(49*log(x)^2-196*x*log(x)+196*x^2),x, algorithm="maxima")

[Out]

-36/49*x^2/(2*x - log(x))

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {-36 x-72 x^2+72 x \log (x)}{196 x^2-196 x \log (x)+49 \log ^2(x)} \, dx=-\frac {36 \, x^{2}}{49 \, {\left (2 \, x - \log \left (x\right )\right )}} \]

[In]

integrate((72*x*log(x)-72*x^2-36*x)/(49*log(x)^2-196*x*log(x)+196*x^2),x, algorithm="giac")

[Out]

-36/49*x^2/(2*x - log(x))

Mupad [B] (verification not implemented)

Time = 9.08 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {-36 x-72 x^2+72 x \log (x)}{196 x^2-196 x \log (x)+49 \log ^2(x)} \, dx=-\frac {36\,x^2}{49\,\left (2\,x-\ln \left (x\right )\right )} \]

[In]

int(-(36*x - 72*x*log(x) + 72*x^2)/(49*log(x)^2 - 196*x*log(x) + 196*x^2),x)

[Out]

-(36*x^2)/(49*(2*x - log(x)))