\(\int (-120+32 x+(-360 x-36 x^2+64 x^3) \log (3)+(144 x^3+120 x^4+24 x^5) \log ^2(3)) \, dx\) [6768]

Optimal result

Integrand size = 43, antiderivative size = 22 \[ \int \left (-120+32 x+\left (-360 x-36 x^2+64 x^3\right ) \log (3)+\left (144 x^3+120 x^4+24 x^5\right ) \log ^2(3)\right ) \, dx=\left (-5+\log \left (e^{-10+4 x+2 x^2 (3+x) \log (3)}\right )\right )^2 \]

[Out]

(ln(exp(2*x+(3+x)*ln(3)*x^2-5)^2)-5)^2

Rubi [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(57\) vs. \(2(22)=44\).

Time = 0.01 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.59, number of steps used = 3, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-120+32 x+\left (-360 x-36 x^2+64 x^3\right ) \log (3)+\left (144 x^3+120 x^4+24 x^5\right ) \log ^2(3)\right ) \, dx=4 x^6 \log ^2(3)+24 x^5 \log ^2(3)+36 x^4 \log ^2(3)+16 x^4 \log (3)-12 x^3 \log (3)+16 x^2-180 x^2 \log (3)-120 x \]

[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{align*} \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{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(58\) vs. \(2(22)=44\).

Time = 0.01 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.64 \[ \int \left (-120+32 x+\left (-360 x-36 x^2+64 x^3\right ) \log (3)+\left (144 x^3+120 x^4+24 x^5\right ) \log ^2(3)\right ) \, dx=4 \left (-30 x+4 x^2-45 x^2 \log (3)-3 x^3 \log (3)+4 x^4 \log (3)+9 x^4 \log ^2(3)+6 x^5 \log ^2(3)+x^6 \log ^2(3)\right ) \]

[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)

Maple [A] (verified)

Time = 0.30 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00

method	result	size
default	\(\left (2 x^{3} \ln \left (3\right )+6 x^{2} \ln \left (3\right )+4 x -15\right )^{2}\)	\(22\)
gosper	\(4 x \left (x^{5} \ln \left (3\right )^{2}+6 x^{4} \ln \left (3\right )^{2}+9 x^{3} \ln \left (3\right )^{2}+4 x^{3} \ln \left (3\right )-3 x^{2} \ln \left (3\right )-45 x \ln \left (3\right )+4 x -30\right )\)	\(54\)
norman	\(\left (36 \ln \left (3\right )^{2}+16 \ln \left (3\right )\right ) x^{4}+\left (-180 \ln \left (3\right )+16\right ) x^{2}-120 x -12 x^{3} \ln \left (3\right )+24 x^{5} \ln \left (3\right )^{2}+4 x^{6} \ln \left (3\right )^{2}\)	\(55\)
risch	\(4 x^{6} \ln \left (3\right )^{2}+24 x^{5} \ln \left (3\right )^{2}+36 x^{4} \ln \left (3\right )^{2}+16 x^{4} \ln \left (3\right )-12 x^{3} \ln \left (3\right )-180 x^{2} \ln \left (3\right )+16 x^{2}-120 x\)	\(58\)
parallelrisch	\(4 x^{6} \ln \left (3\right )^{2}+24 x^{5} \ln \left (3\right )^{2}+36 x^{4} \ln \left (3\right )^{2}+16 x^{4} \ln \left (3\right )-12 x^{3} \ln \left (3\right )-180 x^{2} \ln \left (3\right )+16 x^{2}-120 x\)	\(58\)
parts	\(4 x^{6} \ln \left (3\right )^{2}+24 x^{5} \ln \left (3\right )^{2}+36 x^{4} \ln \left (3\right )^{2}+16 x^{4} \ln \left (3\right )-12 x^{3} \ln \left (3\right )-180 x^{2} \ln \left (3\right )+16 x^{2}-120 x\)	\(58\)

[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]

(2*x^3*ln(3)+6*x^2*ln(3)+4*x-15)^2

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (21) = 42\).

Time = 0.24 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.23 \[ \int \left (-120+32 x+\left (-360 x-36 x^2+64 x^3\right ) \log (3)+\left (144 x^3+120 x^4+24 x^5\right ) \log ^2(3)\right ) \, dx=4 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4}\right )} \log \left (3\right )^{2} + 16 \, x^{2} + 4 \, {\left (4 \, x^{4} - 3 \, x^{3} - 45 \, x^{2}\right )} \log \left (3\right ) - 120 \, x \]

[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

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (22) = 44\).

Time = 0.03 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.55 \[ \int \left (-120+32 x+\left (-360 x-36 x^2+64 x^3\right ) \log (3)+\left (144 x^3+120 x^4+24 x^5\right ) \log ^2(3)\right ) \, dx=4 x^{6} \log {\left (3 \right )}^{2} + 24 x^{5} \log {\left (3 \right )}^{2} + x^{4} \cdot \left (16 \log {\left (3 \right )} + 36 \log {\left (3 \right )}^{2}\right ) - 12 x^{3} \log {\left (3 \right )} + x^{2} \cdot \left (16 - 180 \log {\left (3 \right )}\right ) - 120 x \]

[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

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (21) = 42\).

Time = 0.19 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.23 \[ \int \left (-120+32 x+\left (-360 x-36 x^2+64 x^3\right ) \log (3)+\left (144 x^3+120 x^4+24 x^5\right ) \log ^2(3)\right ) \, dx=4 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4}\right )} \log \left (3\right )^{2} + 16 \, x^{2} + 4 \, {\left (4 \, x^{4} - 3 \, x^{3} - 45 \, x^{2}\right )} \log \left (3\right ) - 120 \, x \]

[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

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (21) = 42\).

Time = 0.27 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.23 \[ \int \left (-120+32 x+\left (-360 x-36 x^2+64 x^3\right ) \log (3)+\left (144 x^3+120 x^4+24 x^5\right ) \log ^2(3)\right ) \, dx=4 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4}\right )} \log \left (3\right )^{2} + 16 \, x^{2} + 4 \, {\left (4 \, x^{4} - 3 \, x^{3} - 45 \, x^{2}\right )} \log \left (3\right ) - 120 \, x \]

[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

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.50 \[ \int \left (-120+32 x+\left (-360 x-36 x^2+64 x^3\right ) \log (3)+\left (144 x^3+120 x^4+24 x^5\right ) \log ^2(3)\right ) \, dx=4\,{\ln \left (3\right )}^2\,x^6+24\,{\ln \left (3\right )}^2\,x^5+\left (16\,\ln \left (3\right )+36\,{\ln \left (3\right )}^2\right )\,x^4-12\,\ln \left (3\right )\,x^3+\left (16-180\,\ln \left (3\right )\right )\,x^2-120\,x \]

[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)