3.60.17 \(\int (1+128 x+816 x^2+1312 x^3+480 x^4+192 x^5+(32 x+192 x^2+256 x^3) \log (2+\log (4))) \, dx\)

Optimal. Leaf size=28 \[ x+x^2 (4+8 x)^2 \left (4+x+\frac {x^2}{2}+\log (2+\log (4))\right ) \]

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Rubi [B]  time = 0.01, antiderivative size = 57, normalized size of antiderivative = 2.04, number of steps used = 2, number of rules used = 0, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 32 x^6+96 x^5+328 x^4+64 x^4 \log (2+\log (4))+272 x^3+64 x^3 \log (2+\log (4))+64 x^2+16 x^2 \log (2+\log (4))+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + 128*x + 816*x^2 + 1312*x^3 + 480*x^4 + 192*x^5 + (32*x + 192*x^2 + 256*x^3)*Log[2 + Log[4]],x]

[Out]

x + 64*x^2 + 272*x^3 + 328*x^4 + 96*x^5 + 32*x^6 + 16*x^2*Log[2 + Log[4]] + 64*x^3*Log[2 + Log[4]] + 64*x^4*Lo
g[2 + Log[4]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x+64 x^2+272 x^3+328 x^4+96 x^5+32 x^6+\log (2+\log (4)) \int \left (32 x+192 x^2+256 x^3\right ) \, dx\\ &=x+64 x^2+272 x^3+328 x^4+96 x^5+32 x^6+16 x^2 \log (2+\log (4))+64 x^3 \log (2+\log (4))+64 x^4 \log (2+\log (4))\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.01, size = 57, normalized size = 2.04 \begin {gather*} x+64 x^2+272 x^3+328 x^4+96 x^5+32 x^6+16 x^2 \log (2+\log (4))+64 x^3 \log (2+\log (4))+64 x^4 \log (2+\log (4)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + 128*x + 816*x^2 + 1312*x^3 + 480*x^4 + 192*x^5 + (32*x + 192*x^2 + 256*x^3)*Log[2 + Log[4]],x]

[Out]

x + 64*x^2 + 272*x^3 + 328*x^4 + 96*x^5 + 32*x^6 + 16*x^2*Log[2 + Log[4]] + 64*x^3*Log[2 + Log[4]] + 64*x^4*Lo
g[2 + Log[4]]

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fricas [A]  time = 0.79, size = 50, normalized size = 1.79 \begin {gather*} 32 \, x^{6} + 96 \, x^{5} + 328 \, x^{4} + 272 \, x^{3} + 64 \, x^{2} + 16 \, {\left (4 \, x^{4} + 4 \, x^{3} + x^{2}\right )} \log \left (2 \, \log \relax (2) + 2\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((256*x^3+192*x^2+32*x)*log(2+2*log(2))+192*x^5+480*x^4+1312*x^3+816*x^2+128*x+1,x, algorithm="fricas
")

[Out]

32*x^6 + 96*x^5 + 328*x^4 + 272*x^3 + 64*x^2 + 16*(4*x^4 + 4*x^3 + x^2)*log(2*log(2) + 2) + x

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giac [A]  time = 0.18, size = 50, normalized size = 1.79 \begin {gather*} 32 \, x^{6} + 96 \, x^{5} + 328 \, x^{4} + 272 \, x^{3} + 64 \, x^{2} + 16 \, {\left (4 \, x^{4} + 4 \, x^{3} + x^{2}\right )} \log \left (2 \, \log \relax (2) + 2\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((256*x^3+192*x^2+32*x)*log(2+2*log(2))+192*x^5+480*x^4+1312*x^3+816*x^2+128*x+1,x, algorithm="giac")

[Out]

32*x^6 + 96*x^5 + 328*x^4 + 272*x^3 + 64*x^2 + 16*(4*x^4 + 4*x^3 + x^2)*log(2*log(2) + 2) + x

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maple [A]  time = 0.05, size = 52, normalized size = 1.86

method	result	size
default	\(\ln \left (2+2 \ln \relax (2)\right ) \left (64 x^{4}+64 x^{3}+16 x^{2}\right )+32 x^{6}+96 x^{5}+328 x^{4}+272 x^{3}+64 x^{2}+x\)	\(52\)
gosper	\(x \left (32 x^{5}+64 \ln \left (2+2 \ln \relax (2)\right ) x^{3}+96 x^{4}+64 \ln \left (2+2 \ln \relax (2)\right ) x^{2}+328 x^{3}+16 \ln \left (2+2 \ln \relax (2)\right ) x +272 x^{2}+64 x +1\right )\)	\(62\)
norman	\(x +\left (16 \ln \relax (2)+16 \ln \left (1+\ln \relax (2)\right )+64\right ) x^{2}+\left (64 \ln \relax (2)+64 \ln \left (1+\ln \relax (2)\right )+272\right ) x^{3}+\left (64 \ln \relax (2)+64 \ln \left (1+\ln \relax (2)\right )+328\right ) x^{4}+96 x^{5}+32 x^{6}\)	\(64\)
risch	\(32 x^{6}+64 x^{4} \ln \relax (2)+64 x^{4} \ln \left (1+\ln \relax (2)\right )+96 x^{5}+64 x^{3} \ln \relax (2)+64 x^{3} \ln \left (1+\ln \relax (2)\right )+328 x^{4}+16 x^{2} \ln \relax (2)+16 x^{2} \ln \left (1+\ln \relax (2)\right )+272 x^{3}+64 x^{2}+x\)	\(79\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((256*x^3+192*x^2+32*x)*ln(2+2*ln(2))+192*x^5+480*x^4+1312*x^3+816*x^2+128*x+1,x,method=_RETURNVERBOSE)

[Out]

ln(2+2*ln(2))*(64*x^4+64*x^3+16*x^2)+32*x^6+96*x^5+328*x^4+272*x^3+64*x^2+x

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maxima [A]  time = 0.36, size = 50, normalized size = 1.79 \begin {gather*} 32 \, x^{6} + 96 \, x^{5} + 328 \, x^{4} + 272 \, x^{3} + 64 \, x^{2} + 16 \, {\left (4 \, x^{4} + 4 \, x^{3} + x^{2}\right )} \log \left (2 \, \log \relax (2) + 2\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((256*x^3+192*x^2+32*x)*log(2+2*log(2))+192*x^5+480*x^4+1312*x^3+816*x^2+128*x+1,x, algorithm="maxima
")

[Out]

32*x^6 + 96*x^5 + 328*x^4 + 272*x^3 + 64*x^2 + 16*(4*x^4 + 4*x^3 + x^2)*log(2*log(2) + 2) + x

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mupad [B]  time = 0.07, size = 57, normalized size = 2.04 \begin {gather*} 32\,x^6+96\,x^5+\left (64\,\ln \left (2\,\ln \relax (2)+2\right )+328\right )\,x^4+\left (64\,\ln \left (2\,\ln \relax (2)+2\right )+272\right )\,x^3+\left (16\,\ln \left (2\,\ln \relax (2)+2\right )+64\right )\,x^2+x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(128*x + log(2*log(2) + 2)*(32*x + 192*x^2 + 256*x^3) + 816*x^2 + 1312*x^3 + 480*x^4 + 192*x^5 + 1,x)

[Out]

x + x^2*(16*log(2*log(2) + 2) + 64) + x^3*(64*log(2*log(2) + 2) + 272) + x^4*(64*log(2*log(2) + 2) + 328) + 96
*x^5 + 32*x^6

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sympy [B]  time = 0.06, size = 56, normalized size = 2.00 \begin {gather*} 32 x^{6} + 96 x^{5} + x^{4} \left (64 \log {\left (2 \log {\relax (2 )} + 2 \right )} + 328\right ) + x^{3} \left (64 \log {\left (2 \log {\relax (2 )} + 2 \right )} + 272\right ) + x^{2} \left (16 \log {\left (2 \log {\relax (2 )} + 2 \right )} + 64\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((256*x**3+192*x**2+32*x)*ln(2+2*ln(2))+192*x**5+480*x**4+1312*x**3+816*x**2+128*x+1,x)

[Out]

32*x**6 + 96*x**5 + x**4*(64*log(2*log(2) + 2) + 328) + x**3*(64*log(2*log(2) + 2) + 272) + x**2*(16*log(2*log
(2) + 2) + 64) + x

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