3.69.83 $\int \frac{-16-7x+31x^2+8x^3-16x^4+(-16-31x^2-16x^3+48x^4)\log (x)}{x^2{\log }^2(x)}dx$

Optimal. Leaf size=33 $$\frac{-x+{(-x+\frac{-1+{(1-2x^2)}^2}{x^2})}^2}{x\log (x)}$$

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Rubi [F]  time = 0.39, 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 = {} $$\begin{array}{c}\int \frac{-16-7x+31x^2+8x^3-16x^4+(-16-31x^2-16x^3+48x^4)\log (x)}{x^2{\log }^2(x)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(-16 - 7*x + 31*x^2 + 8*x^3 - 16*x^4 + (-16 - 31*x^2 - 16*x^3 + 48*x^4)*Log[x])/(x^2*Log[x]^2),x]

[Out]

Defer[Int][(-16 - 7*x + 31*x^2 + 8*x^3 - 16*x^4)/(x^2*Log[x]^2), x] + Defer[Int][(-16 - 31*x^2 - 16*x^3 + 48*x
^4)/(x^2*Log[x]), x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (\frac{-16-7x+31x^2+8x^3-16x^4}{x^2{\log }^2(x)}+\frac{-16-31x^2-16x^3+48x^4}{x^2\log (x)})dx\\ & =\int \frac{-16-7x+31x^2+8x^3-16x^4}{x^2{\log }^2(x)}dx+\int \frac{-16-31x^2-16x^3+48x^4}{x^2\log (x)}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.16, size = 28, normalized size = 0.85 $$\begin{array}{c}\frac{16+7x-31x^2-8x^3+16x^4}{x\log (x)}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-16 - 7*x + 31*x^2 + 8*x^3 - 16*x^4 + (-16 - 31*x^2 - 16*x^3 + 48*x^4)*Log[x])/(x^2*Log[x]^2),x]

[Out]

(16 + 7*x - 31*x^2 - 8*x^3 + 16*x^4)/(x*Log[x])

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fricas [A]  time = 0.59, size = 28, normalized size = 0.85 $$\begin{array}{c}\frac{16x^4-8x^3-31x^2+7x+16}{x\log (x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((48*x^4-16*x^3-31*x^2-16)*log(x)-16*x^4+8*x^3+31*x^2-7*x-16)/x^2/log(x)^2,x, algorithm="fricas")

[Out]

(16*x^4 - 8*x^3 - 31*x^2 + 7*x + 16)/(x*log(x))

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giac [A]  time = 0.15, size = 28, normalized size = 0.85 $$\begin{array}{c}\frac{16x^4-8x^3-31x^2+7x+16}{x\log (x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((48*x^4-16*x^3-31*x^2-16)*log(x)-16*x^4+8*x^3+31*x^2-7*x-16)/x^2/log(x)^2,x, algorithm="giac")

[Out]

(16*x^4 - 8*x^3 - 31*x^2 + 7*x + 16)/(x*log(x))

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maple [A]  time = 0.02, size = 29, normalized size = 0.88

method	result	size
norman	$\frac{16x^4-8x^3-31x^2+7x+16}{x\ln (x)}$	$29$
risch	$\frac{16x^4-8x^3-31x^2+7x+16}{x\ln (x)}$	$29$
default	$\frac{16x^3}{\ln (x)}-\frac{8x^2}{\ln (x)}-\frac{31x}{\ln (x)}+\frac{7}{\ln (x)}+\frac{16}{x\ln (x)}$	$42$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((48*x^4-16*x^3-31*x^2-16)*ln(x)-16*x^4+8*x^3+31*x^2-7*x-16)/x^2/ln(x)^2,x,method=_RETURNVERBOSE)

[Out]

(16*x^4-8*x^3-31*x^2+7*x+16)/x/ln(x)

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maxima [C]  time = 0.42, size = 63, normalized size = 1.91 $$\begin{array}{c}\frac{7}{\log (x)}+48\mathrm{E}\mathrm{i}(3\log (x))-16\mathrm{E}\mathrm{i}(2\log (x))-16\mathrm{E}\mathrm{i}(-\log (x))-31\mathrm{E}\mathrm{i}(\log (x))+31\mathrm{\Gamma }(-1,-\log (x))+16\mathrm{\Gamma }(-1,-2\log (x))-48\mathrm{\Gamma }(-1,-3\log (x))+16\mathrm{\Gamma }(-1,\log (x))\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((48*x^4-16*x^3-31*x^2-16)*log(x)-16*x^4+8*x^3+31*x^2-7*x-16)/x^2/log(x)^2,x, algorithm="maxima")

[Out]

7/log(x) + 48*Ei(3*log(x)) - 16*Ei(2*log(x)) - 16*Ei(-log(x)) - 31*Ei(log(x)) + 31*gamma(-1, -log(x)) + 16*gam
ma(-1, -2*log(x)) - 48*gamma(-1, -3*log(x)) + 16*gamma(-1, log(x))

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mupad [B]  time = 4.17, size = 28, normalized size = 0.85 $$\begin{array}{c}\frac{16x^4-8x^3-31x^2+7x+16}{x\ln (x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(7*x + log(x)*(31*x^2 + 16*x^3 - 48*x^4 + 16) - 31*x^2 - 8*x^3 + 16*x^4 + 16)/(x^2*log(x)^2),x)

[Out]

(7*x - 31*x^2 - 8*x^3 + 16*x^4 + 16)/(x*log(x))

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sympy [A]  time = 0.12, size = 24, normalized size = 0.73 $$\begin{array}{c}\frac{16x^4-8x^3-31x^2+7x+16}{x\log (x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((48*x**4-16*x**3-31*x**2-16)*ln(x)-16*x**4+8*x**3+31*x**2-7*x-16)/x**2/ln(x)**2,x)

[Out]

(16*x**4 - 8*x**3 - 31*x**2 + 7*x + 16)/(x*log(x))

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