3.10.65 \(\int \frac {1+x-2 x^2+4 x^4}{-84 x+x^2-x^3+x^5+x \log (x)} \, dx\) [965]

Optimal. Leaf size=14 \[ \log \left (-84+x-x^2+x^4+\log (x)\right ) \]

[Out]

ln(ln(x)+x^4-x^2+x-84)

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Rubi [F]
time = 0.20, 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 {1+x-2 x^2+4 x^4}{-84 x+x^2-x^3+x^5+x \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1 + x - 2*x^2 + 4*x^4)/(-84*x + x^2 - x^3 + x^5 + x*Log[x]),x]

[Out]

Defer[Int][(-84 + x - x^2 + x^4 + Log[x])^(-1), x] + Defer[Int][1/(x*(-84 + x - x^2 + x^4 + Log[x])), x] - 2*D
efer[Int][x/(-84 + x - x^2 + x^4 + Log[x]), x] + 4*Defer[Int][x^3/(-84 + x - x^2 + x^4 + Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1}{-84+x-x^2+x^4+\log (x)}+\frac {1}{x \left (-84+x-x^2+x^4+\log (x)\right )}-\frac {2 x}{-84+x-x^2+x^4+\log (x)}+\frac {4 x^3}{-84+x-x^2+x^4+\log (x)}\right ) \, dx\\ &=-\left (2 \int \frac {x}{-84+x-x^2+x^4+\log (x)} \, dx\right )+4 \int \frac {x^3}{-84+x-x^2+x^4+\log (x)} \, dx+\int \frac {1}{-84+x-x^2+x^4+\log (x)} \, dx+\int \frac {1}{x \left (-84+x-x^2+x^4+\log (x)\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.03, size = 14, normalized size = 1.00 \begin {gather*} \log \left (-84+x-x^2+x^4+\log (x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 + x - 2*x^2 + 4*x^4)/(-84*x + x^2 - x^3 + x^5 + x*Log[x]),x]

[Out]

Log[-84 + x - x^2 + x^4 + Log[x]]

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Maple [A]
time = 0.25, size = 15, normalized size = 1.07

method	result	size
default	\(\ln \left (\ln \left (x \right )+x^{4}-x^{2}+x -84\right )\)	\(15\)
norman	\(\ln \left (\ln \left (x \right )+x^{4}-x^{2}+x -84\right )\)	\(15\)
risch	\(\ln \left (\ln \left (x \right )+x^{4}-x^{2}+x -84\right )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x^4-2*x^2+x+1)/(x*ln(x)+x^5-x^3+x^2-84*x),x,method=_RETURNVERBOSE)

[Out]

ln(ln(x)+x^4-x^2+x-84)

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Maxima [A]
time = 0.30, size = 14, normalized size = 1.00 \begin {gather*} \log \left (x^{4} - x^{2} + x + \log \left (x\right ) - 84\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^4-2*x^2+x+1)/(x*log(x)+x^5-x^3+x^2-84*x),x, algorithm="maxima")

[Out]

log(x^4 - x^2 + x + log(x) - 84)

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Fricas [A]
time = 0.34, size = 14, normalized size = 1.00 \begin {gather*} \log \left (x^{4} - x^{2} + x + \log \left (x\right ) - 84\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^4-2*x^2+x+1)/(x*log(x)+x^5-x^3+x^2-84*x),x, algorithm="fricas")

[Out]

log(x^4 - x^2 + x + log(x) - 84)

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Sympy [A]
time = 0.07, size = 14, normalized size = 1.00 \begin {gather*} \log {\left (x^{4} - x^{2} + x + \log {\left (x \right )} - 84 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x**4-2*x**2+x+1)/(x*ln(x)+x**5-x**3+x**2-84*x),x)

[Out]

log(x**4 - x**2 + x + log(x) - 84)

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Giac [A]
time = 0.38, size = 14, normalized size = 1.00 \begin {gather*} \log \left (x^{4} - x^{2} + x + \log \left (x\right ) - 84\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^4-2*x^2+x+1)/(x*log(x)+x^5-x^3+x^2-84*x),x, algorithm="giac")

[Out]

log(x^4 - x^2 + x + log(x) - 84)

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Mupad [B]
time = 0.73, size = 14, normalized size = 1.00 \begin {gather*} \ln \left (x+\ln \left (x\right )-x^2+x^4-84\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x - 2*x^2 + 4*x^4 + 1)/(x*log(x) - 84*x + x^2 - x^3 + x^5),x)

[Out]

log(x + log(x) - x^2 + x^4 - 84)

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