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

Optimal. Leaf size=24 \[ x \left (-(x+(1+x) (3+2 x))^2-\log \left (x^2\right )\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 31, normalized size of antiderivative = 1.29, number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {2295} \begin {gather*} -4 x^5-24 x^4-48 x^3-36 x^2-x \log \left (x^2\right )-9 x \end {gather*}

Antiderivative was successfully verified.

[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 2295

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 {gather*} \begin {aligned} \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 {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 31, normalized size = 1.29 \begin {gather*} -9 x-36 x^2-48 x^3-24 x^4-4 x^5-x \log \left (x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[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]

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fricas [A]  time = 0.44, size = 31, normalized size = 1.29 \begin {gather*} -4 \, x^{5} - 24 \, x^{4} - 48 \, x^{3} - 36 \, x^{2} - x \log \left (x^{2}\right ) - 9 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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giac [A]  time = 0.12, size = 31, normalized size = 1.29 \begin {gather*} -4 \, x^{5} - 24 \, x^{4} - 48 \, x^{3} - 36 \, x^{2} - x \log \left (x^{2}\right ) - 9 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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maple [A]  time = 0.02, size = 32, normalized size = 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	\(-4 x^{5}-24 x^{4}-48 x^{3}-36 x^{2}-9 x -x \ln \left (x^{2}\right )\)	\(32\)

Verification of antiderivative is not currently implemented for this CAS.

[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)

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maxima [A]  time = 0.45, size = 31, normalized size = 1.29 \begin {gather*} -4 \, x^{5} - 24 \, x^{4} - 48 \, x^{3} - 36 \, x^{2} - x \log \left (x^{2}\right ) - 9 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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mupad [B]  time = 2.04, size = 27, normalized size = 1.12 \begin {gather*} -x\,\left (36\,x+\ln \left (x^2\right )+48\,x^2+24\,x^3+4\,x^4+9\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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sympy [A]  time = 0.09, size = 31, normalized size = 1.29 \begin {gather*} - 4 x^{5} - 24 x^{4} - 48 x^{3} - 36 x^{2} - x \log {\left (x^{2} \right )} - 9 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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