3.34.92 \(\int \frac {1}{2} (360 x^2-96 x^3-56 x^6+9 x^2 \log (2)) \, dx\)

Optimal. Leaf size=24 \[ 4 x^3 \left (-x^4+3 \left (5-x+\frac {\log (2)}{8}\right )\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 22, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {6, 12} \begin {gather*} -4 x^7-12 x^4+\frac {3}{2} x^3 (40+\log (2)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(360*x^2 - 96*x^3 - 56*x^6 + 9*x^2*Log[2])/2,x]

[Out]

-12*x^4 - 4*x^7 + (3*x^3*(40 + Log[2]))/2

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1}{2} \left (-96 x^3-56 x^6+x^2 (360+9 \log (2))\right ) \, dx\\ &=\frac {1}{2} \int \left (-96 x^3-56 x^6+x^2 (360+9 \log (2))\right ) \, dx\\ &=-12 x^4-4 x^7+\frac {3}{2} x^3 (40+\log (2))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 19, normalized size = 0.79 \begin {gather*} \frac {1}{2} x^3 \left (120-24 x-8 x^4+\log (8)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(360*x^2 - 96*x^3 - 56*x^6 + 9*x^2*Log[2])/2,x]

[Out]

(x^3*(120 - 24*x - 8*x^4 + Log[8]))/2

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fricas [A]  time = 0.50, size = 23, normalized size = 0.96 \begin {gather*} -4 \, x^{7} - 12 \, x^{4} + \frac {3}{2} \, x^{3} \log \relax (2) + 60 \, x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9/2*x^2*log(2)-28*x^6-48*x^3+180*x^2,x, algorithm="fricas")

[Out]

-4*x^7 - 12*x^4 + 3/2*x^3*log(2) + 60*x^3

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giac [A]  time = 0.24, size = 23, normalized size = 0.96 \begin {gather*} -4 \, x^{7} - 12 \, x^{4} + \frac {3}{2} \, x^{3} \log \relax (2) + 60 \, x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9/2*x^2*log(2)-28*x^6-48*x^3+180*x^2,x, algorithm="giac")

[Out]

-4*x^7 - 12*x^4 + 3/2*x^3*log(2) + 60*x^3

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maple [A]  time = 0.02, size = 20, normalized size = 0.83

method	result	size
gosper	\(\frac {x^{3} \left (-8 x^{4}+3 \ln \relax (2)-24 x +120\right )}{2}\)	\(20\)
norman	\(\left (\frac {3 \ln \relax (2)}{2}+60\right ) x^{3}-12 x^{4}-4 x^{7}\)	\(22\)
default	\(\frac {3 x^{3} \ln \relax (2)}{2}-4 x^{7}-12 x^{4}+60 x^{3}\)	\(24\)
risch	\(\frac {3 x^{3} \ln \relax (2)}{2}-4 x^{7}-12 x^{4}+60 x^{3}\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(9/2*x^2*ln(2)-28*x^6-48*x^3+180*x^2,x,method=_RETURNVERBOSE)

[Out]

1/2*x^3*(-8*x^4+3*ln(2)-24*x+120)

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maxima [A]  time = 0.57, size = 23, normalized size = 0.96 \begin {gather*} -4 \, x^{7} - 12 \, x^{4} + \frac {3}{2} \, x^{3} \log \relax (2) + 60 \, x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9/2*x^2*log(2)-28*x^6-48*x^3+180*x^2,x, algorithm="maxima")

[Out]

-4*x^7 - 12*x^4 + 3/2*x^3*log(2) + 60*x^3

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mupad [B]  time = 0.04, size = 19, normalized size = 0.79 \begin {gather*} -\frac {x^3\,\left (24\,x^4+72\,x-\ln \left (512\right )-360\right )}{6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((9*x^2*log(2))/2 + 180*x^2 - 48*x^3 - 28*x^6,x)

[Out]

-(x^3*(72*x - log(512) + 24*x^4 - 360))/6

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sympy [A]  time = 0.06, size = 20, normalized size = 0.83 \begin {gather*} - 4 x^{7} - 12 x^{4} + x^{3} \left (\frac {3 \log {\relax (2 )}}{2} + 60\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9/2*x**2*ln(2)-28*x**6-48*x**3+180*x**2,x)

[Out]

-4*x**7 - 12*x**4 + x**3*(3*log(2)/2 + 60)

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