\(\int (-11-72 x-144 x^2-96 x^3-20 x^4-\log (x^2)) \, dx\) [3516]

Optimal result

Integrand size = 26, antiderivative size = 24 \[ \int \left (-11-72 x-144 x^2-96 x^3-20 x^4-\log \left (x^2\right )\right ) \, dx=x \left (-(x+(1+x) (3+2 x))^2-\log \left (x^2\right )\right ) \]

[Out]

x*(-ln(x^2)-((3+2*x)*(1+x)+x)^2)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {2332} \[ \int \left (-11-72 x-144 x^2-96 x^3-20 x^4-\log \left (x^2\right )\right ) \, dx=-4 x^5-24 x^4-48 x^3-36 x^2-x \log \left (x^2\right )-9 x \]

[In]

Int[-11 - 72*x - 144*x^2 - 96*x^3 - 20*x^4 - Log[x^2],x]

[Out]

-9*x - 36*x^2 - 48*x^3 - 24*x^4 - 4*x^5 - x*Log[x^2]

Rule 2332

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rubi steps \begin{align*} \text {integral}& = -11 x-36 x^2-48 x^3-24 x^4-4 x^5-\int \log \left (x^2\right ) \, dx \\ & = -9 x-36 x^2-48 x^3-24 x^4-4 x^5-x \log \left (x^2\right ) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \left (-11-72 x-144 x^2-96 x^3-20 x^4-\log \left (x^2\right )\right ) \, dx=-9 x-36 x^2-48 x^3-24 x^4-4 x^5-x \log \left (x^2\right ) \]

[In]

Integrate[-11 - 72*x - 144*x^2 - 96*x^3 - 20*x^4 - Log[x^2],x]

[Out]

-9*x - 36*x^2 - 48*x^3 - 24*x^4 - 4*x^5 - x*Log[x^2]

Maple [A] (verified)

Time = 0.20 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.33

method	result	size
default	\(-4 x^{5}-24 x^{4}-48 x^{3}-36 x^{2}-9 x -x \ln \left (x^{2}\right )\)	\(32\)
norman	\(-4 x^{5}-24 x^{4}-48 x^{3}-36 x^{2}-9 x -x \ln \left (x^{2}\right )\)	\(32\)
risch	\(-4 x^{5}-24 x^{4}-48 x^{3}-36 x^{2}-9 x -x \ln \left (x^{2}\right )\)	\(32\)
parallelrisch	\(-4 x^{5}-24 x^{4}-48 x^{3}-36 x^{2}-9 x -x \ln \left (x^{2}\right )\)	\(32\)
parts	\(-4 x^{5}-24 x^{4}-48 x^{3}-36 x^{2}-9 x -x \ln \left (x^{2}\right )\)	\(32\)

[In]

int(-ln(x^2)-20*x^4-96*x^3-144*x^2-72*x-11,x,method=_RETURNVERBOSE)

[Out]

-4*x^5-24*x^4-48*x^3-36*x^2-9*x-x*ln(x^2)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \left (-11-72 x-144 x^2-96 x^3-20 x^4-\log \left (x^2\right )\right ) \, dx=-4 \, x^{5} - 24 \, x^{4} - 48 \, x^{3} - 36 \, x^{2} - x \log \left (x^{2}\right ) - 9 \, x \]

[In]

integrate(-log(x^2)-20*x^4-96*x^3-144*x^2-72*x-11,x, algorithm="fricas")

[Out]

-4*x^5 - 24*x^4 - 48*x^3 - 36*x^2 - x*log(x^2) - 9*x

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \left (-11-72 x-144 x^2-96 x^3-20 x^4-\log \left (x^2\right )\right ) \, dx=- 4 x^{5} - 24 x^{4} - 48 x^{3} - 36 x^{2} - x \log {\left (x^{2} \right )} - 9 x \]

[In]

integrate(-ln(x**2)-20*x**4-96*x**3-144*x**2-72*x-11,x)

[Out]

-4*x**5 - 24*x**4 - 48*x**3 - 36*x**2 - x*log(x**2) - 9*x

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \left (-11-72 x-144 x^2-96 x^3-20 x^4-\log \left (x^2\right )\right ) \, dx=-4 \, x^{5} - 24 \, x^{4} - 48 \, x^{3} - 36 \, x^{2} - x \log \left (x^{2}\right ) - 9 \, x \]

[In]

integrate(-log(x^2)-20*x^4-96*x^3-144*x^2-72*x-11,x, algorithm="maxima")

[Out]

-4*x^5 - 24*x^4 - 48*x^3 - 36*x^2 - x*log(x^2) - 9*x

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \left (-11-72 x-144 x^2-96 x^3-20 x^4-\log \left (x^2\right )\right ) \, dx=-4 \, x^{5} - 24 \, x^{4} - 48 \, x^{3} - 36 \, x^{2} - x \log \left (x^{2}\right ) - 9 \, x \]

[In]

integrate(-log(x^2)-20*x^4-96*x^3-144*x^2-72*x-11,x, algorithm="giac")

[Out]

-4*x^5 - 24*x^4 - 48*x^3 - 36*x^2 - x*log(x^2) - 9*x

Mupad [B] (verification not implemented)

Time = 9.12 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \left (-11-72 x-144 x^2-96 x^3-20 x^4-\log \left (x^2\right )\right ) \, dx=-x\,\left (36\,x+\ln \left (x^2\right )+48\,x^2+24\,x^3+4\,x^4+9\right ) \]

[In]

int(- 72*x - log(x^2) - 144*x^2 - 96*x^3 - 20*x^4 - 11,x)

[Out]

-x*(36*x + log(x^2) + 48*x^2 + 24*x^3 + 4*x^4 + 9)