3.72.23 \(\int \frac {e^{289+25 \log ^2(x)} (171-50 \log (x))}{x^{170} (\frac {e^{289+25 \log ^2(x)}}{x^{169}}+x^2)} \, dx\)

Optimal. Leaf size=19 \[ \log \left (\frac {x}{e^{(3+5 (-4+\log (x)))^2}+x}\right ) \]

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Rubi [F]  time = 1.06, 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 {e^{289+25 \log ^2(x)} (171-50 \log (x))}{x^{170} \left (\frac {e^{289+25 \log ^2(x)}}{x^{169}}+x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(289 + 25*Log[x]^2)*(171 - 50*Log[x]))/(x^170*(E^(289 + 25*Log[x]^2)/x^169 + x^2)),x]

[Out]

171*Defer[Int][E^(289 + 25*Log[x]^2)/(E^(289 + 25*Log[x]^2)*x + x^172), x] - 50*Defer[Int][(E^(289 + 25*Log[x]
^2)*Log[x])/(E^(289 + 25*Log[x]^2)*x + x^172), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {171 e^{289+25 \log ^2(x)}}{e^{289+25 \log ^2(x)} x+x^{172}}-\frac {50 e^{289+25 \log ^2(x)} \log (x)}{e^{289+25 \log ^2(x)} x+x^{172}}\right ) \, dx\\ &=-\left (50 \int \frac {e^{289+25 \log ^2(x)} \log (x)}{e^{289+25 \log ^2(x)} x+x^{172}} \, dx\right )+171 \int \frac {e^{289+25 \log ^2(x)}}{e^{289+25 \log ^2(x)} x+x^{172}} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.16, size = 22, normalized size = 1.16 \begin {gather*} 171 \log (x)-\log \left (e^{289+25 \log ^2(x)}+x^{171}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(289 + 25*Log[x]^2)*(171 - 50*Log[x]))/(x^170*(E^(289 + 25*Log[x]^2)/x^169 + x^2)),x]

[Out]

171*Log[x] - Log[E^(289 + 25*Log[x]^2) + x^171]

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fricas [A]  time = 0.86, size = 21, normalized size = 1.11 \begin {gather*} -\log \left (x + e^{\left (25 \, \log \relax (x)^{2} - 170 \, \log \relax (x) + 289\right )}\right ) + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-50*log(x)+171)*exp(25*log(x)^2-170*log(x)+289)/(x*exp(25*log(x)^2-170*log(x)+289)+x^2),x, algorith
m="fricas")

[Out]

-log(x + e^(25*log(x)^2 - 170*log(x) + 289)) + log(x)

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giac [A]  time = 0.21, size = 21, normalized size = 1.11 \begin {gather*} -\log \left (x^{171} + e^{\left (25 \, \log \relax (x)^{2} + 289\right )}\right ) + 171 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-50*log(x)+171)*exp(25*log(x)^2-170*log(x)+289)/(x*exp(25*log(x)^2-170*log(x)+289)+x^2),x, algorith
m="giac")

[Out]

-log(x^171 + e^(25*log(x)^2 + 289)) + 171*log(x)

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maple [A]  time = 0.03, size = 22, normalized size = 1.16

method	result	size
norman	\(\ln \relax (x )-\ln \left ({\mathrm e}^{25 \ln \relax (x )^{2}-170 \ln \relax (x )+289}+x \right )\)	\(22\)
risch	\(\ln \relax (x )+289-\ln \left (\frac {{\mathrm e}^{25 \ln \relax (x )^{2}+289}}{x^{170}}+x \right )\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-50*ln(x)+171)*exp(25*ln(x)^2-170*ln(x)+289)/(x*exp(25*ln(x)^2-170*ln(x)+289)+x^2),x,method=_RETURNVERBOS
E)

[Out]

ln(x)-ln(exp(25*ln(x)^2-170*ln(x)+289)+x)

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maxima [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-50*log(x)+171)*exp(25*log(x)^2-170*log(x)+289)/(x*exp(25*log(x)^2-170*log(x)+289)+x^2),x, algorith
m="maxima")

[Out]

Timed out

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mupad [B]  time = 4.45, size = 22, normalized size = 1.16 \begin {gather*} \ln \left (x^{171}\right )-\ln \left ({\mathrm {e}}^{25\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{289}+x^{171}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(25*log(x)^2 - 170*log(x) + 289)*(50*log(x) - 171))/(x*exp(25*log(x)^2 - 170*log(x) + 289) + x^2),x)

[Out]

log(x^171) - log(exp(25*log(x)^2)*exp(289) + x^171)

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sympy [A]  time = 0.32, size = 19, normalized size = 1.00 \begin {gather*} 171 \log {\relax (x )} - \log {\left (x^{171} + e^{25 \log {\relax (x )}^{2} + 289} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-50*ln(x)+171)*exp(25*ln(x)**2-170*ln(x)+289)/(x*exp(25*ln(x)**2-170*ln(x)+289)+x**2),x)

[Out]

171*log(x) - log(x**171 + exp(25*log(x)**2 + 289))

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