\(\int \frac {1}{3} (-13824-19956 x-5408 x^2+(2304+1664 x) \log (2)-96 \log ^2(2)) \, dx\) [6692]

Optimal result

Integrand size = 28, antiderivative size = 24 \[ \int \frac {1}{3} \left (-13824-19956 x-5408 x^2+(2304+1664 x) \log (2)-96 \log ^2(2)\right ) \, dx=2 x \left (x-16 \left (\frac {x}{3}+4 (3+x)-\log (2)\right )^2\right ) \]

[Out]

2*(x-16*(13/3*x-ln(2)+12)^2)*x

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.46, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {12} \[ \int \frac {1}{3} \left (-13824-19956 x-5408 x^2+(2304+1664 x) \log (2)-96 \log ^2(2)\right ) \, dx=-\frac {5408 x^3}{9}-3326 x^2-32 x \left (144+\log ^2(2)\right )+\frac {64}{39} (13 x+18)^2 \log (2) \]

[In]

Int[(-13824 - 19956*x - 5408*x^2 + (2304 + 1664*x)*Log[2] - 96*Log[2]^2)/3,x]

[Out]

-3326*x^2 - (5408*x^3)/9 + (64*(18 + 13*x)^2*Log[2])/39 - 32*x*(144 + Log[2]^2)

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{align*} \text {integral}& = \frac {1}{3} \int \left (-13824-19956 x-5408 x^2+(2304+1664 x) \log (2)-96 \log ^2(2)\right ) \, dx \\ & = -3326 x^2-\frac {5408 x^3}{9}+\frac {64}{39} (18+13 x)^2 \log (2)-32 x \left (144+\log ^2(2)\right ) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.46 \[ \int \frac {1}{3} \left (-13824-19956 x-5408 x^2+(2304+1664 x) \log (2)-96 \log ^2(2)\right ) \, dx=-\frac {4}{3} \left (\frac {4989 x^2}{2}+\frac {1352 x^3}{3}+24 x (-12+\log (2))^2-208 x^2 \log (2)\right ) \]

[In]

Integrate[(-13824 - 19956*x - 5408*x^2 + (2304 + 1664*x)*Log[2] - 96*Log[2]^2)/3,x]

[Out]

(-4*((4989*x^2)/2 + (1352*x^3)/3 + 24*x*(-12 + Log[2])^2 - 208*x^2*Log[2]))/3

Maple [A] (verified)

Time = 0.08 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.21

method	result	size
gosper	\(-\frac {2 x \left (144 \ln \left (2\right )^{2}-1248 x \ln \left (2\right )+2704 x^{2}-3456 \ln \left (2\right )+14967 x +20736\right )}{9}\)	\(29\)
norman	\(\left (\frac {832 \ln \left (2\right )}{3}-3326\right ) x^{2}+\left (-32 \ln \left (2\right )^{2}+768 \ln \left (2\right )-4608\right ) x -\frac {5408 x^{3}}{9}\)	\(31\)
default	\(-32 x \ln \left (2\right )^{2}+\frac {832 x^{2} \ln \left (2\right )}{3}-\frac {5408 x^{3}}{9}+768 x \ln \left (2\right )-3326 x^{2}-4608 x\)	\(34\)
risch	\(-32 x \ln \left (2\right )^{2}+\frac {832 x^{2} \ln \left (2\right )}{3}-\frac {5408 x^{3}}{9}+768 x \ln \left (2\right )-3326 x^{2}-4608 x\)	\(34\)
parallelrisch	\(-\frac {5408 x^{3}}{9}+\frac {832 x^{2} \ln \left (2\right )}{3}-3326 x^{2}+768 x \ln \left (2\right )+\left (-32 \ln \left (2\right )^{2}-4608\right ) x\)	\(34\)
parts	\(-32 x \ln \left (2\right )^{2}+\frac {832 x^{2} \ln \left (2\right )}{3}-\frac {5408 x^{3}}{9}+768 x \ln \left (2\right )-3326 x^{2}-4608 x\)	\(34\)

[In]

int(-32*ln(2)^2+1/3*(1664*x+2304)*ln(2)-5408/3*x^2-6652*x-4608,x,method=_RETURNVERBOSE)

[Out]

-2/9*x*(144*ln(2)^2-1248*x*ln(2)+2704*x^2-3456*ln(2)+14967*x+20736)

Fricas [A] (verification not implemented)

none

Time = 0.50 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.42 \[ \int \frac {1}{3} \left (-13824-19956 x-5408 x^2+(2304+1664 x) \log (2)-96 \log ^2(2)\right ) \, dx=-\frac {5408}{9} \, x^{3} - 32 \, x \log \left (2\right )^{2} - 3326 \, x^{2} + \frac {64}{3} \, {\left (13 \, x^{2} + 36 \, x\right )} \log \left (2\right ) - 4608 \, x \]

[In]

integrate(-32*log(2)^2+1/3*(1664*x+2304)*log(2)-5408/3*x^2-6652*x-4608,x, algorithm="fricas")

[Out]

-5408/9*x^3 - 32*x*log(2)^2 - 3326*x^2 + 64/3*(13*x^2 + 36*x)*log(2) - 4608*x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.33 \[ \int \frac {1}{3} \left (-13824-19956 x-5408 x^2+(2304+1664 x) \log (2)-96 \log ^2(2)\right ) \, dx=- \frac {5408 x^{3}}{9} + x^{2} \left (-3326 + \frac {832 \log {\left (2 \right )}}{3}\right ) + x \left (-4608 - 32 \log {\left (2 \right )}^{2} + 768 \log {\left (2 \right )}\right ) \]

[In]

integrate(-32*ln(2)**2+1/3*(1664*x+2304)*ln(2)-5408/3*x**2-6652*x-4608,x)

[Out]

-5408*x**3/9 + x**2*(-3326 + 832*log(2)/3) + x*(-4608 - 32*log(2)**2 + 768*log(2))

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.42 \[ \int \frac {1}{3} \left (-13824-19956 x-5408 x^2+(2304+1664 x) \log (2)-96 \log ^2(2)\right ) \, dx=-\frac {5408}{9} \, x^{3} - 32 \, x \log \left (2\right )^{2} - 3326 \, x^{2} + \frac {64}{3} \, {\left (13 \, x^{2} + 36 \, x\right )} \log \left (2\right ) - 4608 \, x \]

[In]

integrate(-32*log(2)^2+1/3*(1664*x+2304)*log(2)-5408/3*x^2-6652*x-4608,x, algorithm="maxima")

[Out]

-5408/9*x^3 - 32*x*log(2)^2 - 3326*x^2 + 64/3*(13*x^2 + 36*x)*log(2) - 4608*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.42 \[ \int \frac {1}{3} \left (-13824-19956 x-5408 x^2+(2304+1664 x) \log (2)-96 \log ^2(2)\right ) \, dx=-\frac {5408}{9} \, x^{3} - 32 \, x \log \left (2\right )^{2} - 3326 \, x^{2} + \frac {64}{3} \, {\left (13 \, x^{2} + 36 \, x\right )} \log \left (2\right ) - 4608 \, x \]

[In]

integrate(-32*log(2)^2+1/3*(1664*x+2304)*log(2)-5408/3*x^2-6652*x-4608,x, algorithm="giac")

[Out]

-5408/9*x^3 - 32*x*log(2)^2 - 3326*x^2 + 64/3*(13*x^2 + 36*x)*log(2) - 4608*x

Mupad [B] (verification not implemented)

Time = 12.53 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \frac {1}{3} \left (-13824-19956 x-5408 x^2+(2304+1664 x) \log (2)-96 \log ^2(2)\right ) \, dx=-\frac {5408\,x^3}{9}+\left (\frac {832\,\ln \left (2\right )}{3}-3326\right )\,x^2+\left (768\,\ln \left (2\right )-32\,{\ln \left (2\right )}^2-4608\right )\,x \]

[In]

int((log(2)*(1664*x + 2304))/3 - 6652*x - 32*log(2)^2 - (5408*x^2)/3 - 4608,x)

[Out]

x^2*((832*log(2))/3 - 3326) - x*(32*log(2)^2 - 768*log(2) + 4608) - (5408*x^3)/9