3.26.33 \(\int \frac {64 \log ^3(\log (\frac {26 x}{25}))+16 \log (\frac {26 x}{25}) \log ^4(\log (\frac {26 x}{25}))}{\log (\frac {26 x}{25})} \, dx\)

Optimal. Leaf size=12 \[ 16 x \log ^4\left (\log \left (\frac {26 x}{25}\right )\right ) \]

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Rubi [F]  time = 0.17, 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 {64 \log ^3\left (\log \left (\frac {26 x}{25}\right )\right )+16 \log \left (\frac {26 x}{25}\right ) \log ^4\left (\log \left (\frac {26 x}{25}\right )\right )}{\log \left (\frac {26 x}{25}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(64*Log[Log[(26*x)/25]]^3 + 16*Log[(26*x)/25]*Log[Log[(26*x)/25]]^4)/Log[(26*x)/25],x]

[Out]

(800*Defer[Subst][Defer[Int][Log[Log[x]]^3/Log[x], x], x, (26*x)/25])/13 + (200*Defer[Subst][Defer[Int][Log[Lo
g[x]]^4, x], x, (26*x)/25])/13

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {25}{26} \operatorname {Subst}\left (\int \frac {64 \log ^3(\log (x))+16 \log (x) \log ^4(\log (x))}{\log (x)} \, dx,x,\frac {26 x}{25}\right )\\ &=\frac {25}{26} \operatorname {Subst}\left (\int \frac {16 \log ^3(\log (x)) (4+\log (x) \log (\log (x)))}{\log (x)} \, dx,x,\frac {26 x}{25}\right )\\ &=\frac {200}{13} \operatorname {Subst}\left (\int \frac {\log ^3(\log (x)) (4+\log (x) \log (\log (x)))}{\log (x)} \, dx,x,\frac {26 x}{25}\right )\\ &=\frac {200}{13} \operatorname {Subst}\left (\int \left (\frac {4 \log ^3(\log (x))}{\log (x)}+\log ^4(\log (x))\right ) \, dx,x,\frac {26 x}{25}\right )\\ &=\frac {200}{13} \operatorname {Subst}\left (\int \log ^4(\log (x)) \, dx,x,\frac {26 x}{25}\right )+\frac {800}{13} \operatorname {Subst}\left (\int \frac {\log ^3(\log (x))}{\log (x)} \, dx,x,\frac {26 x}{25}\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 12, normalized size = 1.00 \begin {gather*} 16 x \log ^4\left (\log \left (\frac {26 x}{25}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(64*Log[Log[(26*x)/25]]^3 + 16*Log[(26*x)/25]*Log[Log[(26*x)/25]]^4)/Log[(26*x)/25],x]

[Out]

16*x*Log[Log[(26*x)/25]]^4

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fricas [A]  time = 0.58, size = 10, normalized size = 0.83 \begin {gather*} 16 \, x \log \left (\log \left (\frac {26}{25} \, x\right )\right )^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*log(26/25*x)*log(log(26/25*x))^4+64*log(log(26/25*x))^3)/log(26/25*x),x, algorithm="fricas")

[Out]

16*x*log(log(26/25*x))^4

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giac [A]  time = 0.33, size = 10, normalized size = 0.83 \begin {gather*} 16 \, x \log \left (\log \left (\frac {26}{25} \, x\right )\right )^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*log(26/25*x)*log(log(26/25*x))^4+64*log(log(26/25*x))^3)/log(26/25*x),x, algorithm="giac")

[Out]

16*x*log(log(26/25*x))^4

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maple [A]  time = 0.05, size = 11, normalized size = 0.92

method	result	size
norman	\(16 \ln \left (\ln \left (\frac {26 x}{25}\right )\right )^{4} x\)	\(11\)
risch	\(16 \ln \left (\ln \left (\frac {26 x}{25}\right )\right )^{4} x\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((16*ln(26/25*x)*ln(ln(26/25*x))^4+64*ln(ln(26/25*x))^3)/ln(26/25*x),x,method=_RETURNVERBOSE)

[Out]

16*ln(ln(26/25*x))^4*x

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maxima [A]  time = 0.46, size = 10, normalized size = 0.83 \begin {gather*} 16 \, x \log \left (\log \left (\frac {26}{25} \, x\right )\right )^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*log(26/25*x)*log(log(26/25*x))^4+64*log(log(26/25*x))^3)/log(26/25*x),x, algorithm="maxima")

[Out]

16*x*log(log(26/25*x))^4

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mupad [B]  time = 1.64, size = 10, normalized size = 0.83 \begin {gather*} 16\,x\,{\ln \left (\ln \left (\frac {26\,x}{25}\right )\right )}^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((64*log(log((26*x)/25))^3 + 16*log((26*x)/25)*log(log((26*x)/25))^4)/log((26*x)/25),x)

[Out]

16*x*log(log((26*x)/25))^4

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sympy [A]  time = 0.31, size = 12, normalized size = 1.00 \begin {gather*} 16 x \log {\left (\log {\left (\frac {26 x}{25} \right )} \right )}^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*ln(26/25*x)*ln(ln(26/25*x))**4+64*ln(ln(26/25*x))**3)/ln(26/25*x),x)

[Out]

16*x*log(log(26*x/25))**4

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