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

Optimal. Leaf size=15 \[ \frac {36 x^2}{49 (-2 x+\log (x))} \]

________________________________________________________________________________________

Rubi [F]  time = 0.38, 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 {-36 x-72 x^2+72 x \log (x)}{196 x^2-196 x \log (x)+49 \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[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 {gather*} \begin {aligned} \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 {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.08, size = 15, normalized size = 1.00 \begin {gather*} \frac {36 x^2}{49 (-2 x+\log (x))} \end {gather*}

Antiderivative was successfully verified.

[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]))

________________________________________________________________________________________

fricas [A]  time = 0.64, size = 15, normalized size = 1.00 \begin {gather*} -\frac {36 \, x^{2}}{49 \, {\left (2 \, x - \log \relax (x)\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

________________________________________________________________________________________

giac [A]  time = 0.20, size = 15, normalized size = 1.00 \begin {gather*} -\frac {36 \, x^{2}}{49 \, {\left (2 \, x - \log \relax (x)\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

________________________________________________________________________________________

maple [A]  time = 0.02, size = 16, normalized size = 1.07

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

Verification of antiderivative is not currently implemented for this CAS.

[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/(2*x-ln(x))

________________________________________________________________________________________

maxima [A]  time = 0.38, size = 15, normalized size = 1.00 \begin {gather*} -\frac {36 \, x^{2}}{49 \, {\left (2 \, x - \log \relax (x)\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

________________________________________________________________________________________

mupad [B]  time = 2.05, size = 15, normalized size = 1.00 \begin {gather*} -\frac {36\,x^2}{49\,\left (2\,x-\ln \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)))

________________________________________________________________________________________

sympy [A]  time = 0.10, size = 12, normalized size = 0.80 \begin {gather*} \frac {36 x^{2}}{- 98 x + 49 \log {\relax (x )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

________________________________________________________________________________________