3.16.75 \(\int (576 x^7-1296 x^{15}+\log (\log (3))) \, dx\)

Optimal. Leaf size=18 \[ 2-\left (4-9 x^8\right )^2+x \log (\log (3)) \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.89, number of steps used = 1, number of rules used = 0, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -81 x^{16}+72 x^8+x \log (\log (3)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[576*x^7 - 1296*x^15 + Log[Log[3]],x]

[Out]

72*x^8 - 81*x^16 + x*Log[Log[3]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=72 x^8-81 x^{16}+x \log (\log (3))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.89 \begin {gather*} 72 x^8-81 x^{16}+x \log (\log (3)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[576*x^7 - 1296*x^15 + Log[Log[3]],x]

[Out]

72*x^8 - 81*x^16 + x*Log[Log[3]]

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fricas [A]  time = 0.62, size = 16, normalized size = 0.89 \begin {gather*} -81 \, x^{16} + 72 \, x^{8} + x \log \left (\log \relax (3)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(log(3))-1296*x^15+576*x^7,x, algorithm="fricas")

[Out]

-81*x^16 + 72*x^8 + x*log(log(3))

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giac [A]  time = 0.14, size = 16, normalized size = 0.89 \begin {gather*} -81 \, x^{16} + 72 \, x^{8} + x \log \left (\log \relax (3)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(log(3))-1296*x^15+576*x^7,x, algorithm="giac")

[Out]

-81*x^16 + 72*x^8 + x*log(log(3))

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maple [A]  time = 0.04, size = 17, normalized size = 0.94

method	result	size
gosper	\(\ln \left (\ln \relax (3)\right ) x +72 x^{8}-81 x^{16}\)	\(17\)
default	\(\ln \left (\ln \relax (3)\right ) x +72 x^{8}-81 x^{16}\)	\(17\)
norman	\(\ln \left (\ln \relax (3)\right ) x +72 x^{8}-81 x^{16}\)	\(17\)
risch	\(\ln \left (\ln \relax (3)\right ) x +72 x^{8}-81 x^{16}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(ln(3))-1296*x^15+576*x^7,x,method=_RETURNVERBOSE)

[Out]

ln(ln(3))*x+72*x^8-81*x^16

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maxima [A]  time = 0.36, size = 16, normalized size = 0.89 \begin {gather*} -81 \, x^{16} + 72 \, x^{8} + x \log \left (\log \relax (3)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(log(3))-1296*x^15+576*x^7,x, algorithm="maxima")

[Out]

-81*x^16 + 72*x^8 + x*log(log(3))

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mupad [B]  time = 0.03, size = 16, normalized size = 0.89 \begin {gather*} x\,\left (-81\,x^{15}+72\,x^7+\ln \left (\ln \relax (3)\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(log(3)) + 576*x^7 - 1296*x^15,x)

[Out]

x*(log(log(3)) + 72*x^7 - 81*x^15)

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sympy [A]  time = 0.06, size = 15, normalized size = 0.83 \begin {gather*} - 81 x^{16} + 72 x^{8} + x \log {\left (\log {\relax (3 )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(ln(3))-1296*x**15+576*x**7,x)

[Out]

-81*x**16 + 72*x**8 + x*log(log(3))

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