3.68.68 \(\int (-120+32 x+(-360 x-36 x^2+64 x^3) \log (3)+(144 x^3+120 x^4+24 x^5) \log ^2(3)) \, dx\)

Optimal. Leaf size=22 \[ \left (-5+\log \left (e^{-10+4 x+2 x^2 (3+x) \log (3)}\right )\right )^2 \]

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Rubi [B]  time = 0.02, antiderivative size = 57, normalized size of antiderivative = 2.59, number of steps used = 3, number of rules used = 0, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 4 x^6 \log ^2(3)+24 x^5 \log ^2(3)+36 x^4 \log ^2(3)+16 x^4 \log (3)-12 x^3 \log (3)+16 x^2-180 x^2 \log (3)-120 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-120 + 32*x + (-360*x - 36*x^2 + 64*x^3)*Log[3] + (144*x^3 + 120*x^4 + 24*x^5)*Log[3]^2,x]

[Out]

-120*x + 16*x^2 - 180*x^2*Log[3] - 12*x^3*Log[3] + 16*x^4*Log[3] + 36*x^4*Log[3]^2 + 24*x^5*Log[3]^2 + 4*x^6*L
og[3]^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-120 x+16 x^2+\log (3) \int \left (-360 x-36 x^2+64 x^3\right ) \, dx+\log ^2(3) \int \left (144 x^3+120 x^4+24 x^5\right ) \, dx\\ &=-120 x+16 x^2-180 x^2 \log (3)-12 x^3 \log (3)+16 x^4 \log (3)+36 x^4 \log ^2(3)+24 x^5 \log ^2(3)+4 x^6 \log ^2(3)\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.01, size = 58, normalized size = 2.64 \begin {gather*} 4 \left (-30 x+4 x^2-45 x^2 \log (3)-3 x^3 \log (3)+4 x^4 \log (3)+9 x^4 \log ^2(3)+6 x^5 \log ^2(3)+x^6 \log ^2(3)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-120 + 32*x + (-360*x - 36*x^2 + 64*x^3)*Log[3] + (144*x^3 + 120*x^4 + 24*x^5)*Log[3]^2,x]

[Out]

4*(-30*x + 4*x^2 - 45*x^2*Log[3] - 3*x^3*Log[3] + 4*x^4*Log[3] + 9*x^4*Log[3]^2 + 6*x^5*Log[3]^2 + x^6*Log[3]^
2)

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fricas [B]  time = 0.59, size = 49, normalized size = 2.23 \begin {gather*} 4 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4}\right )} \log \relax (3)^{2} + 16 \, x^{2} + 4 \, {\left (4 \, x^{4} - 3 \, x^{3} - 45 \, x^{2}\right )} \log \relax (3) - 120 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x^5+120*x^4+144*x^3)*log(3)^2+(64*x^3-36*x^2-360*x)*log(3)+32*x-120,x, algorithm="fricas")

[Out]

4*(x^6 + 6*x^5 + 9*x^4)*log(3)^2 + 16*x^2 + 4*(4*x^4 - 3*x^3 - 45*x^2)*log(3) - 120*x

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giac [B]  time = 0.23, size = 49, normalized size = 2.23 \begin {gather*} 4 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4}\right )} \log \relax (3)^{2} + 16 \, x^{2} + 4 \, {\left (4 \, x^{4} - 3 \, x^{3} - 45 \, x^{2}\right )} \log \relax (3) - 120 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x^5+120*x^4+144*x^3)*log(3)^2+(64*x^3-36*x^2-360*x)*log(3)+32*x-120,x, algorithm="giac")

[Out]

4*(x^6 + 6*x^5 + 9*x^4)*log(3)^2 + 16*x^2 + 4*(4*x^4 - 3*x^3 - 45*x^2)*log(3) - 120*x

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maple [B]  time = 0.03, size = 50, normalized size = 2.27

method	result	size
default	\(\ln \relax (3)^{2} \left (4 x^{6}+24 x^{5}+36 x^{4}\right )+\ln \relax (3) \left (16 x^{4}-12 x^{3}-180 x^{2}\right )+16 x^{2}-120 x\)	\(50\)
gosper	\(4 x \left (x^{5} \ln \relax (3)^{2}+6 x^{4} \ln \relax (3)^{2}+9 x^{3} \ln \relax (3)^{2}+4 x^{3} \ln \relax (3)-3 x^{2} \ln \relax (3)-45 x \ln \relax (3)+4 x -30\right )\)	\(54\)
norman	\(\left (36 \ln \relax (3)^{2}+16 \ln \relax (3)\right ) x^{4}+\left (-180 \ln \relax (3)+16\right ) x^{2}-120 x -12 x^{3} \ln \relax (3)+24 x^{5} \ln \relax (3)^{2}+4 x^{6} \ln \relax (3)^{2}\)	\(55\)
risch	\(4 x^{6} \ln \relax (3)^{2}+24 x^{5} \ln \relax (3)^{2}+36 x^{4} \ln \relax (3)^{2}+16 x^{4} \ln \relax (3)-12 x^{3} \ln \relax (3)-180 x^{2} \ln \relax (3)+16 x^{2}-120 x\)	\(58\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((24*x^5+120*x^4+144*x^3)*ln(3)^2+(64*x^3-36*x^2-360*x)*ln(3)+32*x-120,x,method=_RETURNVERBOSE)

[Out]

ln(3)^2*(4*x^6+24*x^5+36*x^4)+ln(3)*(16*x^4-12*x^3-180*x^2)+16*x^2-120*x

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maxima [B]  time = 0.50, size = 49, normalized size = 2.23 \begin {gather*} 4 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4}\right )} \log \relax (3)^{2} + 16 \, x^{2} + 4 \, {\left (4 \, x^{4} - 3 \, x^{3} - 45 \, x^{2}\right )} \log \relax (3) - 120 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x^5+120*x^4+144*x^3)*log(3)^2+(64*x^3-36*x^2-360*x)*log(3)+32*x-120,x, algorithm="maxima")

[Out]

4*(x^6 + 6*x^5 + 9*x^4)*log(3)^2 + 16*x^2 + 4*(4*x^4 - 3*x^3 - 45*x^2)*log(3) - 120*x

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mupad [B]  time = 4.10, size = 55, normalized size = 2.50 \begin {gather*} 4\,{\ln \relax (3)}^2\,x^6+24\,{\ln \relax (3)}^2\,x^5+\left (16\,\ln \relax (3)+36\,{\ln \relax (3)}^2\right )\,x^4-12\,\ln \relax (3)\,x^3+\left (16-180\,\ln \relax (3)\right )\,x^2-120\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32*x + log(3)^2*(144*x^3 + 120*x^4 + 24*x^5) - log(3)*(360*x + 36*x^2 - 64*x^3) - 120,x)

[Out]

24*x^5*log(3)^2 - 120*x + 4*x^6*log(3)^2 - x^2*(180*log(3) - 16) + x^4*(16*log(3) + 36*log(3)^2) - 12*x^3*log(
3)

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sympy [B]  time = 0.06, size = 56, normalized size = 2.55 \begin {gather*} 4 x^{6} \log {\relax (3 )}^{2} + 24 x^{5} \log {\relax (3 )}^{2} + x^{4} \left (16 \log {\relax (3 )} + 36 \log {\relax (3 )}^{2}\right ) - 12 x^{3} \log {\relax (3 )} + x^{2} \left (16 - 180 \log {\relax (3 )}\right ) - 120 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x**5+120*x**4+144*x**3)*ln(3)**2+(64*x**3-36*x**2-360*x)*ln(3)+32*x-120,x)

[Out]

4*x**6*log(3)**2 + 24*x**5*log(3)**2 + x**4*(16*log(3) + 36*log(3)**2) - 12*x**3*log(3) + x**2*(16 - 180*log(3
)) - 120*x

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