3.95.46 $\int \frac{112-288x+144x^2-240x^4-12\log (x)}{49-434x+1465x^2-2400x^3+2040x^4-696x^5-600x^6+864x^7-288x^8+144x^{10}+(42x-186x^2+216x^3-72x^4+72x^6)\log (x)+9x^2{\log }^2(x)}dx$

Optimal. Leaf size=30 $$\frac{4}{7-x(4+3((3-2x{)}^2-4x^4-\log (x)))}$$

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Rubi [A]  time = 0.42, antiderivative size = 29, normalized size of antiderivative = 0.97, number of steps used = 3, number of rules used = 3, integrand size = 103, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.029, Rules used = {6688, 12, 6686} $$\begin{array}{c}\frac{4}{12x^5-12x^3+36x^2-31x+3x\log (x)+7}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(112 - 288*x + 144*x^2 - 240*x^4 - 12*Log[x])/(49 - 434*x + 1465*x^2 - 2400*x^3 + 2040*x^4 - 696*x^5 - 600
*x^6 + 864*x^7 - 288*x^8 + 144*x^10 + (42*x - 186*x^2 + 216*x^3 - 72*x^4 + 72*x^6)*Log[x] + 9*x^2*Log[x]^2),x]

[Out]

4/(7 - 31*x + 36*x^2 - 12*x^3 + 12*x^5 + 3*x*Log[x])

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 6686

Int[(u_)*(y_)^(m_.), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Simp[(q*y^(m + 1))/(m + 1), x] /;  !F
alseQ[q]] /; FreeQ[m, x] && NeQ[m, -1]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{4(28-72x+36x^2-60x^4-3\log (x))}{{(7-31x+36x^2-12x^3+12x^5+3x\log (x))}^2}dx\\ & =4\int \frac{28-72x+36x^2-60x^4-3\log (x)}{{(7-31x+36x^2-12x^3+12x^5+3x\log (x))}^2}dx\\ & =\frac{4}{7-31x+36x^2-12x^3+12x^5+3x\log (x)}\end{array}\end{array}$$

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Mathematica [A]  time = 0.03, size = 29, normalized size = 0.97 $$\begin{array}{c}\frac{4}{7-31x+36x^2-12x^3+12x^5+3x\log (x)}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(112 - 288*x + 144*x^2 - 240*x^4 - 12*Log[x])/(49 - 434*x + 1465*x^2 - 2400*x^3 + 2040*x^4 - 696*x^5
- 600*x^6 + 864*x^7 - 288*x^8 + 144*x^10 + (42*x - 186*x^2 + 216*x^3 - 72*x^4 + 72*x^6)*Log[x] + 9*x^2*Log[x]
^2),x]

[Out]

4/(7 - 31*x + 36*x^2 - 12*x^3 + 12*x^5 + 3*x*Log[x])

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fricas [A]  time = 0.56, size = 29, normalized size = 0.97 $$\begin{array}{c}\frac{4}{12x^5-12x^3+36x^2+3x\log (x)-31x+7}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*log(x)-240*x^4+144*x^2-288*x+112)/(9*x^2*log(x)^2+(72*x^6-72*x^4+216*x^3-186*x^2+42*x)*log(x)+1
44*x^10-288*x^8+864*x^7-600*x^6-696*x^5+2040*x^4-2400*x^3+1465*x^2-434*x+49),x, algorithm="fricas")

[Out]

4/(12*x^5 - 12*x^3 + 36*x^2 + 3*x*log(x) - 31*x + 7)

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giac [A]  time = 0.16, size = 29, normalized size = 0.97 $$\begin{array}{c}\frac{4}{12x^5-12x^3+36x^2+3x\log (x)-31x+7}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*log(x)-240*x^4+144*x^2-288*x+112)/(9*x^2*log(x)^2+(72*x^6-72*x^4+216*x^3-186*x^2+42*x)*log(x)+1
44*x^10-288*x^8+864*x^7-600*x^6-696*x^5+2040*x^4-2400*x^3+1465*x^2-434*x+49),x, algorithm="giac")

[Out]

4/(12*x^5 - 12*x^3 + 36*x^2 + 3*x*log(x) - 31*x + 7)

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maple [A]  time = 0.03, size = 30, normalized size = 1.00

method	result	size
risch	$\frac{4}{12x^5-12x^3+3x\ln (x)+36x^2-31x+7}$	$30$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-12*ln(x)-240*x^4+144*x^2-288*x+112)/(9*x^2*ln(x)^2+(72*x^6-72*x^4+216*x^3-186*x^2+42*x)*ln(x)+144*x^10-2
88*x^8+864*x^7-600*x^6-696*x^5+2040*x^4-2400*x^3+1465*x^2-434*x+49),x,method=_RETURNVERBOSE)

[Out]

4/(12*x^5-12*x^3+3*x*ln(x)+36*x^2-31*x+7)

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maxima [A]  time = 0.37, size = 29, normalized size = 0.97 $$\begin{array}{c}\frac{4}{12x^5-12x^3+36x^2+3x\log (x)-31x+7}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*log(x)-240*x^4+144*x^2-288*x+112)/(9*x^2*log(x)^2+(72*x^6-72*x^4+216*x^3-186*x^2+42*x)*log(x)+1
44*x^10-288*x^8+864*x^7-600*x^6-696*x^5+2040*x^4-2400*x^3+1465*x^2-434*x+49),x, algorithm="maxima")

[Out]

4/(12*x^5 - 12*x^3 + 36*x^2 + 3*x*log(x) - 31*x + 7)

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mupad [B]  time = 7.66, size = 29, normalized size = 0.97 $$\begin{array}{c}\frac{4}{x(3\ln (x)-31)+36x^2-12x^3+12x^5+7}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(288*x + 12*log(x) - 144*x^2 + 240*x^4 - 112)/(log(x)*(42*x - 186*x^2 + 216*x^3 - 72*x^4 + 72*x^6) - 434*
x + 9*x^2*log(x)^2 + 1465*x^2 - 2400*x^3 + 2040*x^4 - 696*x^5 - 600*x^6 + 864*x^7 - 288*x^8 + 144*x^10 + 49),x
)

[Out]

4/(x*(3*log(x) - 31) + 36*x^2 - 12*x^3 + 12*x^5 + 7)

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sympy [A]  time = 0.22, size = 27, normalized size = 0.90 $$\begin{array}{c}\frac{4}{12x^5-12x^3+36x^2+3x\log (x)-31x+7}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*ln(x)-240*x**4+144*x**2-288*x+112)/(9*x**2*ln(x)**2+(72*x**6-72*x**4+216*x**3-186*x**2+42*x)*ln
(x)+144*x**10-288*x**8+864*x**7-600*x**6-696*x**5+2040*x**4-2400*x**3+1465*x**2-434*x+49),x)

[Out]

4/(12*x**5 - 12*x**3 + 36*x**2 + 3*x*log(x) - 31*x + 7)

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