3.68.15 \(\int (40+32 x+(-60 x^2-64 x^3) \log ^2(4)+24 x^5 \log ^4(4)) \, dx\)

Optimal. Leaf size=19 \[ \left (-3+2 \left (-1-2 x+x^3 \log ^2(4)\right )\right )^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 36, normalized size of antiderivative = 1.89, number of steps used = 2, number of rules used = 0, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 4 x^6 \log ^4(4)-16 x^4 \log ^2(4)-20 x^3 \log ^2(4)+16 x^2+40 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[40 + 32*x + (-60*x^2 - 64*x^3)*Log[4]^2 + 24*x^5*Log[4]^4,x]

[Out]

40*x + 16*x^2 - 20*x^3*Log[4]^2 - 16*x^4*Log[4]^2 + 4*x^6*Log[4]^4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=40 x+16 x^2+4 x^6 \log ^4(4)+\log ^2(4) \int \left (-60 x^2-64 x^3\right ) \, dx\\ &=40 x+16 x^2-20 x^3 \log ^2(4)-16 x^4 \log ^2(4)+4 x^6 \log ^4(4)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 36, normalized size = 1.89 \begin {gather*} 40 x+16 x^2-20 x^3 \log ^2(4)-16 x^4 \log ^2(4)+4 x^6 \log ^4(4) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[40 + 32*x + (-60*x^2 - 64*x^3)*Log[4]^2 + 24*x^5*Log[4]^4,x]

[Out]

40*x + 16*x^2 - 20*x^3*Log[4]^2 - 16*x^4*Log[4]^2 + 4*x^6*Log[4]^4

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fricas [B]  time = 0.61, size = 35, normalized size = 1.84 \begin {gather*} 64 \, x^{6} \log \relax (2)^{4} - 16 \, {\left (4 \, x^{4} + 5 \, x^{3}\right )} \log \relax (2)^{2} + 16 \, x^{2} + 40 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(384*x^5*log(2)^4+4*(-64*x^3-60*x^2)*log(2)^2+32*x+40,x, algorithm="fricas")

[Out]

64*x^6*log(2)^4 - 16*(4*x^4 + 5*x^3)*log(2)^2 + 16*x^2 + 40*x

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giac [B]  time = 0.12, size = 35, normalized size = 1.84 \begin {gather*} 64 \, x^{6} \log \relax (2)^{4} - 16 \, {\left (4 \, x^{4} + 5 \, x^{3}\right )} \log \relax (2)^{2} + 16 \, x^{2} + 40 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(384*x^5*log(2)^4+4*(-64*x^3-60*x^2)*log(2)^2+32*x+40,x, algorithm="giac")

[Out]

64*x^6*log(2)^4 - 16*(4*x^4 + 5*x^3)*log(2)^2 + 16*x^2 + 40*x

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maple [B]  time = 0.03, size = 36, normalized size = 1.89

method	result	size
gosper	\(8 x \left (8 x^{5} \ln \relax (2)^{4}-8 x^{3} \ln \relax (2)^{2}-10 x^{2} \ln \relax (2)^{2}+2 x +5\right )\)	\(36\)
default	\(64 x^{6} \ln \relax (2)^{4}+4 \ln \relax (2)^{2} \left (-16 x^{4}-20 x^{3}\right )+16 x^{2}+40 x\)	\(36\)
norman	\(40 x +16 x^{2}-80 x^{3} \ln \relax (2)^{2}-64 x^{4} \ln \relax (2)^{2}+64 x^{6} \ln \relax (2)^{4}\)	\(37\)
risch	\(40 x +16 x^{2}-80 x^{3} \ln \relax (2)^{2}-64 x^{4} \ln \relax (2)^{2}+64 x^{6} \ln \relax (2)^{4}\)	\(37\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(384*x^5*ln(2)^4+4*(-64*x^3-60*x^2)*ln(2)^2+32*x+40,x,method=_RETURNVERBOSE)

[Out]

8*x*(8*x^5*ln(2)^4-8*x^3*ln(2)^2-10*x^2*ln(2)^2+2*x+5)

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maxima [B]  time = 0.35, size = 35, normalized size = 1.84 \begin {gather*} 64 \, x^{6} \log \relax (2)^{4} - 16 \, {\left (4 \, x^{4} + 5 \, x^{3}\right )} \log \relax (2)^{2} + 16 \, x^{2} + 40 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(384*x^5*log(2)^4+4*(-64*x^3-60*x^2)*log(2)^2+32*x+40,x, algorithm="maxima")

[Out]

64*x^6*log(2)^4 - 16*(4*x^4 + 5*x^3)*log(2)^2 + 16*x^2 + 40*x

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mupad [B]  time = 3.99, size = 36, normalized size = 1.89 \begin {gather*} 64\,{\ln \relax (2)}^4\,x^6-64\,{\ln \relax (2)}^2\,x^4-80\,{\ln \relax (2)}^2\,x^3+16\,x^2+40\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32*x + 384*x^5*log(2)^4 - 4*log(2)^2*(60*x^2 + 64*x^3) + 40,x)

[Out]

40*x - 80*x^3*log(2)^2 - 64*x^4*log(2)^2 + 64*x^6*log(2)^4 + 16*x^2

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sympy [B]  time = 0.06, size = 37, normalized size = 1.95 \begin {gather*} 64 x^{6} \log {\relax (2 )}^{4} - 64 x^{4} \log {\relax (2 )}^{2} - 80 x^{3} \log {\relax (2 )}^{2} + 16 x^{2} + 40 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(384*x**5*ln(2)**4+4*(-64*x**3-60*x**2)*ln(2)**2+32*x+40,x)

[Out]

64*x**6*log(2)**4 - 64*x**4*log(2)**2 - 80*x**3*log(2)**2 + 16*x**2 + 40*x

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