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

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

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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 = {} $$\begin{array}{c}\int \frac{-36x-72x^2+72x\log (x)}{196x^2-196x\log (x)+49{\log }^2(x)}dx\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{36x(-1-2x+2\log (x))}{49(2x-\log (x){)}^2}dx\\ & =\frac{36}{49}\int \frac{x(-1-2x+2\log (x))}{(2x-\log (x){)}^2}dx\\ & =\frac{36}{49}\int (\frac{x(-1+2x)}{(2x-\log (x){)}^2}-\frac{2x}{2x-\log (x)})dx\\ & =\frac{36}{49}\int \frac{x(-1+2x)}{(2x-\log (x){)}^2}dx-\frac{72}{49}\int \frac{x}{2x-\log (x)}dx\\ & =\frac{36}{49}\int (-\frac{x}{(2x-\log (x){)}^2}+\frac{2x^2}{(2x-\log (x){)}^2})dx-\frac{72}{49}\int \frac{x}{2x-\log (x)}dx\\ & =-(\frac{36}{49}\int \frac{x}{(2x-\log (x){)}^2}dx)+\frac{72}{49}\int \frac{x^2}{(2x-\log (x){)}^2}dx-\frac{72}{49}\int \frac{x}{2x-\log (x)}dx\end{array}\end{array}$$

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

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]))

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fricas [A]  time = 0.64, size = 15, normalized size = 1.00 $$\begin{array}{c}-\frac{36x^2}{49(2x-\log (x))}\end{array}$$

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))

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giac [A]  time = 0.20, size = 15, normalized size = 1.00 $$\begin{array}{c}-\frac{36x^2}{49(2x-\log (x))}\end{array}$$

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))

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

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

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))

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maxima [A]  time = 0.38, size = 15, normalized size = 1.00 $$\begin{array}{c}-\frac{36x^2}{49(2x-\log (x))}\end{array}$$

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))

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mupad [B]  time = 2.05, size = 15, normalized size = 1.00 $$\begin{array}{c}-\frac{36x^2}{49(2x-\ln (x))}\end{array}$$

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)))

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

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))

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