3.64.95 \(\int \frac {180 x-308 x^2-272 x^3-21 x^4+(-150+280 x+255 x^2+20 x^3) \log (2)+(30 x-56 x^2-51 x^3-4 x^4+(-30+56 x+51 x^2+4 x^3) \log (2)) \log (x-\log (2))}{-3 x+3 \log (2)} \, dx\)

Optimal. Leaf size=26 \[ \left (5+\frac {x}{3}\right ) x \left (-2+2 x+x^2\right ) (5+\log (x-\log (2))) \]

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Rubi [B]  time = 0.56, antiderivative size = 299, normalized size of antiderivative = 11.50, number of steps used = 17, number of rules used = 7, integrand size = 93, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.075, Rules used = {6742, 1850, 2417, 2389, 2295, 2395, 43} \begin {gather*} \frac {5 x^4}{3}+\frac {1}{3} x^4 \log (x-\log (2))-\frac {17 x^3}{9}+\frac {17}{3} x^3 \log (x-\log (2))+\frac {1}{9} x^3 (272+\log (2))-\frac {1}{9} x^3 \log (2)-\frac {14 x^2}{3}+\frac {1}{18} x^2 \left (924+7 \log ^2(8)-765 \log (2)+4 \log (8) (68-\log (32))\right )-\frac {1}{6} x^2 \log ^2(2)+\frac {28}{3} x^2 \log (x-\log (2))-\frac {17}{6} x^2 \log (2)+10 x-\frac {1}{3} \log ^4(2) \log (x-\log (2))-\frac {1}{3} x \log ^3(2)-\frac {17}{3} \log ^3(2) \log (x-\log (2))-\frac {17}{3} x \log ^2(2)-\frac {28}{3} \log ^2(2) \log (x-\log (2))-\frac {1}{27} x \left (1620-7 \log ^3(8)-4 \log ^2(8) (68-\log (32))-924 \log (8)+45 \log (2) (56+17 \log (8))\right )-\frac {1}{27} \log (2) \left (270-7 \log ^3(8)-\log ^2(8) (17-4 \log (32))-84 \log (8)\right ) \log (3 x-\log (8))-\frac {28}{3} x \log (2)-10 (x-\log (2)) \log (x-\log (2)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(180*x - 308*x^2 - 272*x^3 - 21*x^4 + (-150 + 280*x + 255*x^2 + 20*x^3)*Log[2] + (30*x - 56*x^2 - 51*x^3 -
4*x^4 + (-30 + 56*x + 51*x^2 + 4*x^3)*Log[2])*Log[x - Log[2]])/(-3*x + 3*Log[2]),x]

[Out]

10*x - (14*x^2)/3 - (17*x^3)/9 + (5*x^4)/3 - (28*x*Log[2])/3 - (17*x^2*Log[2])/6 - (x^3*Log[2])/9 - (17*x*Log[
2]^2)/3 - (x^2*Log[2]^2)/6 - (x*Log[2]^3)/3 + (x^3*(272 + Log[2]))/9 + (x^2*(924 - 765*Log[2] + 7*Log[8]^2 + 4
*Log[8]*(68 - Log[32])))/18 - (x*(1620 - 924*Log[8] - 7*Log[8]^3 + 45*Log[2]*(56 + 17*Log[8]) - 4*Log[8]^2*(68
- Log[32])))/27 + (28*x^2*Log[x - Log[2]])/3 + (17*x^3*Log[x - Log[2]])/3 + (x^4*Log[x - Log[2]])/3 - 10*(x -
Log[2])*Log[x - Log[2]] - (28*Log[2]^2*Log[x - Log[2]])/3 - (17*Log[2]^3*Log[x - Log[2]])/3 - (Log[2]^4*Log[x
- Log[2]])/3 - (Log[2]*(270 - 84*Log[8] - 7*Log[8]^3 - Log[8]^2*(17 - 4*Log[32]))*Log[3*x - Log[8]])/27

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rule 1850

Int[(Pq_)*((a_) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] :> Int[ExpandIntegrand[Pq*(a + b*x^n)^p, x], x] /; FreeQ[
{a, b, n}, x] && PolyQ[Pq, x] && (IGtQ[p, 0] || EqQ[n, 1])

Rule 2295

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

Rule 2389

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.), x_Symbol] :> Dist[1/e, Subst[Int[(a + b*Log[c*
x^n])^p, x], x, d + e*x], x] /; FreeQ[{a, b, c, d, e, n, p}, x]

Rule 2395

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))*((f_.) + (g_.)*(x_))^(q_.), x_Symbol] :> Simp[((f + g
*x)^(q + 1)*(a + b*Log[c*(d + e*x)^n]))/(g*(q + 1)), x] - Dist[(b*e*n)/(g*(q + 1)), Int[(f + g*x)^(q + 1)/(d +
e*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, n, q}, x] && NeQ[e*f - d*g, 0] && NeQ[q, -1]

Rule 2417

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*(Polyx_), x_Symbol] :> Int[ExpandIntegrand[Poly
x*(a + b*Log[c*(d + e*x)^n])^p, x], x] /; FreeQ[{a, b, c, d, e, n, p}, x] && PolynomialQ[Polyx, x]

Rule 6742

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {21 x^4+x^2 (308-255 \log (2))+150 \log (2)-20 x (9+14 \log (2))+4 x^3 (68-\log (32))}{3 x-\log (8)}+\frac {1}{3} \left (-30+56 x+51 x^2+4 x^3\right ) \log (x-\log (2))\right ) \, dx\\ &=\frac {1}{3} \int \left (-30+56 x+51 x^2+4 x^3\right ) \log (x-\log (2)) \, dx+\int \frac {21 x^4+x^2 (308-255 \log (2))+150 \log (2)-20 x (9+14 \log (2))+4 x^3 (68-\log (32))}{3 x-\log (8)} \, dx\\ &=\frac {1}{3} \int \left (-30 \log (x-\log (2))+56 x \log (x-\log (2))+51 x^2 \log (x-\log (2))+4 x^3 \log (x-\log (2))\right ) \, dx+\int \left (7 x^3+\frac {1}{3} x^2 (272+\log (2))+\frac {45 \log (2) \left (90-56 \log (8)-17 \log ^2(8)\right )-\log (8) \left (1620-924 \log (8)-7 \log ^3(8)-4 \log ^2(8) (68-\log (32))\right )}{27 (3 x-\log (8))}+\frac {1}{9} x \left (924-765 \log (2)+7 \log ^2(8)+4 \log (8) (68-\log (32))\right )+\frac {1}{27} \left (-1620+924 \log (8)+7 \log ^3(8)-45 \log (2) (56+17 \log (8))+4 \log ^2(8) (68-\log (32))\right )\right ) \, dx\\ &=\frac {7 x^4}{4}+\frac {1}{9} x^3 (272+\log (2))+\frac {1}{18} x^2 \left (924-765 \log (2)+7 \log ^2(8)+4 \log (8) (68-\log (32))\right )-\frac {1}{27} x \left (1620-924 \log (8)-7 \log ^3(8)+45 \log (2) (56+17 \log (8))-4 \log ^2(8) (68-\log (32))\right )-\frac {1}{27} \log (2) \left (270-84 \log (8)-7 \log ^3(8)-\log ^2(8) (17-4 \log (32))\right ) \log (3 x-\log (8))+\frac {4}{3} \int x^3 \log (x-\log (2)) \, dx-10 \int \log (x-\log (2)) \, dx+17 \int x^2 \log (x-\log (2)) \, dx+\frac {56}{3} \int x \log (x-\log (2)) \, dx\\ &=\frac {7 x^4}{4}+\frac {1}{9} x^3 (272+\log (2))+\frac {1}{18} x^2 \left (924-765 \log (2)+7 \log ^2(8)+4 \log (8) (68-\log (32))\right )-\frac {1}{27} x \left (1620-924 \log (8)-7 \log ^3(8)+45 \log (2) (56+17 \log (8))-4 \log ^2(8) (68-\log (32))\right )+\frac {28}{3} x^2 \log (x-\log (2))+\frac {17}{3} x^3 \log (x-\log (2))+\frac {1}{3} x^4 \log (x-\log (2))-\frac {1}{27} \log (2) \left (270-84 \log (8)-7 \log ^3(8)-\log ^2(8) (17-4 \log (32))\right ) \log (3 x-\log (8))-\frac {1}{3} \int \frac {x^4}{x-\log (2)} \, dx-\frac {17}{3} \int \frac {x^3}{x-\log (2)} \, dx-\frac {28}{3} \int \frac {x^2}{x-\log (2)} \, dx-10 \operatorname {Subst}(\int \log (x) \, dx,x,x-\log (2))\\ &=10 x+\frac {7 x^4}{4}+\frac {1}{9} x^3 (272+\log (2))+\frac {1}{18} x^2 \left (924-765 \log (2)+7 \log ^2(8)+4 \log (8) (68-\log (32))\right )-\frac {1}{27} x \left (1620-924 \log (8)-7 \log ^3(8)+45 \log (2) (56+17 \log (8))-4 \log ^2(8) (68-\log (32))\right )+\frac {28}{3} x^2 \log (x-\log (2))+\frac {17}{3} x^3 \log (x-\log (2))+\frac {1}{3} x^4 \log (x-\log (2))-10 (x-\log (2)) \log (x-\log (2))-\frac {1}{27} \log (2) \left (270-84 \log (8)-7 \log ^3(8)-\log ^2(8) (17-4 \log (32))\right ) \log (3 x-\log (8))-\frac {1}{3} \int \left (x^3+x^2 \log (2)+x \log ^2(2)+\log ^3(2)+\frac {\log ^4(2)}{x-\log (2)}\right ) \, dx-\frac {17}{3} \int \left (x^2+x \log (2)+\log ^2(2)+\frac {\log ^3(2)}{x-\log (2)}\right ) \, dx-\frac {28}{3} \int \left (x+\log (2)+\frac {\log ^2(2)}{x-\log (2)}\right ) \, dx\\ &=10 x-\frac {14 x^2}{3}-\frac {17 x^3}{9}+\frac {5 x^4}{3}-\frac {28}{3} x \log (2)-\frac {17}{6} x^2 \log (2)-\frac {1}{9} x^3 \log (2)-\frac {17}{3} x \log ^2(2)-\frac {1}{6} x^2 \log ^2(2)-\frac {1}{3} x \log ^3(2)+\frac {1}{9} x^3 (272+\log (2))+\frac {1}{18} x^2 \left (924-765 \log (2)+7 \log ^2(8)+4 \log (8) (68-\log (32))\right )-\frac {1}{27} x \left (1620-924 \log (8)-7 \log ^3(8)+45 \log (2) (56+17 \log (8))-4 \log ^2(8) (68-\log (32))\right )+\frac {28}{3} x^2 \log (x-\log (2))+\frac {17}{3} x^3 \log (x-\log (2))+\frac {1}{3} x^4 \log (x-\log (2))-10 (x-\log (2)) \log (x-\log (2))-\frac {28}{3} \log ^2(2) \log (x-\log (2))-\frac {17}{3} \log ^3(2) \log (x-\log (2))-\frac {1}{3} \log ^4(2) \log (x-\log (2))-\frac {1}{27} \log (2) \left (270-84 \log (8)-7 \log ^3(8)-\log ^2(8) (17-4 \log (32))\right ) \log (3 x-\log (8))\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.43, size = 157, normalized size = 6.04 \begin {gather*} \frac {1}{162} \left (3 x \left (-2700+1530 x^2+90 x^3-306 \log ^2(2)-18 \log ^3(2)+\log (4) \log ^2(8)+x \left (2520-9 \log ^2(2)+\log ^2(8)\right )+\log (8) \log (5070602400912917605986812821504)\right )+54 \left (-30 x+28 x^2+17 x^3+x^4-\log (2) \left (-30+28 \log (2)+17 \log ^2(2)+\log ^3(2)\right )\right ) \log (x-\log (2))-2 \left (45 \log (2) \left (-90+56 \log (8)+17 \log ^2(8)\right )+\log (8) \left (1620-924 \log (8)-7 \log ^3(8)+4 \log ^2(8) (-68+\log (32))\right )\right ) \log (3 x-\log (8))\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(180*x - 308*x^2 - 272*x^3 - 21*x^4 + (-150 + 280*x + 255*x^2 + 20*x^3)*Log[2] + (30*x - 56*x^2 - 51
*x^3 - 4*x^4 + (-30 + 56*x + 51*x^2 + 4*x^3)*Log[2])*Log[x - Log[2]])/(-3*x + 3*Log[2]),x]

[Out]

(3*x*(-2700 + 1530*x^2 + 90*x^3 - 306*Log[2]^2 - 18*Log[2]^3 + Log[4]*Log[8]^2 + x*(2520 - 9*Log[2]^2 + Log[8]
^2) + Log[8]*Log[5070602400912917605986812821504]) + 54*(-30*x + 28*x^2 + 17*x^3 + x^4 - Log[2]*(-30 + 28*Log[
2] + 17*Log[2]^2 + Log[2]^3))*Log[x - Log[2]] - 2*(45*Log[2]*(-90 + 56*Log[8] + 17*Log[8]^2) + Log[8]*(1620 -
924*Log[8] - 7*Log[8]^3 + 4*Log[8]^2*(-68 + Log[32])))*Log[3*x - Log[8]])/162

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fricas [A]  time = 0.58, size = 45, normalized size = 1.73 \begin {gather*} \frac {5}{3} \, x^{4} + \frac {85}{3} \, x^{3} + \frac {140}{3} \, x^{2} + \frac {1}{3} \, {\left (x^{4} + 17 \, x^{3} + 28 \, x^{2} - 30 \, x\right )} \log \left (x - \log \relax (2)\right ) - 50 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^3+51*x^2+56*x-30)*log(2)-4*x^4-51*x^3-56*x^2+30*x)*log(x-log(2))+(20*x^3+255*x^2+280*x-150)*l
og(2)-21*x^4-272*x^3-308*x^2+180*x)/(3*log(2)-3*x),x, algorithm="fricas")

[Out]

5/3*x^4 + 85/3*x^3 + 140/3*x^2 + 1/3*(x^4 + 17*x^3 + 28*x^2 - 30*x)*log(x - log(2)) - 50*x

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giac [A]  time = 0.23, size = 45, normalized size = 1.73 \begin {gather*} \frac {5}{3} \, x^{4} + \frac {85}{3} \, x^{3} + \frac {140}{3} \, x^{2} + \frac {1}{3} \, {\left (x^{4} + 17 \, x^{3} + 28 \, x^{2} - 30 \, x\right )} \log \left (x - \log \relax (2)\right ) - 50 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^3+51*x^2+56*x-30)*log(2)-4*x^4-51*x^3-56*x^2+30*x)*log(x-log(2))+(20*x^3+255*x^2+280*x-150)*l
og(2)-21*x^4-272*x^3-308*x^2+180*x)/(3*log(2)-3*x),x, algorithm="giac")

[Out]

5/3*x^4 + 85/3*x^3 + 140/3*x^2 + 1/3*(x^4 + 17*x^3 + 28*x^2 - 30*x)*log(x - log(2)) - 50*x

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maple [A]  time = 0.42, size = 47, normalized size = 1.81

method	result	size
risch	\(\left (\frac {1}{3} x^{4}+\frac {17}{3} x^{3}+\frac {28}{3} x^{2}-10 x \right ) \ln \left (x -\ln \relax (2)\right )+\frac {5 x^{4}}{3}+\frac {85 x^{3}}{3}+\frac {140 x^{2}}{3}-50 x\)	\(47\)
norman	\(-50 x +\frac {140 x^{2}}{3}+\frac {85 x^{3}}{3}+\frac {5 x^{4}}{3}-10 \ln \left (x -\ln \relax (2)\right ) x +\frac {28 \ln \left (x -\ln \relax (2)\right ) x^{2}}{3}+\frac {17 \ln \left (x -\ln \relax (2)\right ) x^{3}}{3}+\frac {\ln \left (x -\ln \relax (2)\right ) x^{4}}{3}\)	\(66\)
derivativedivides	\(-50 x +50 \ln \relax (2)+11 \ln \relax (2)^{2} \left (x -\ln \relax (2)\right )^{2}+\frac {140 \left (x -\ln \relax (2)\right )^{2}}{3}+\frac {28 \ln \relax (2)^{2} \ln \left (x -\ln \relax (2)\right )}{3}-10 \ln \relax (2) \ln \left (x -\ln \relax (2)\right )+\frac {\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )^{4}}{3}+8 \ln \relax (2)^{3} \left (x -\ln \relax (2)\right )+\frac {64 \ln \relax (2) \left (x -\ln \relax (2)\right )^{3}}{9}+\frac {17 \ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )^{3}}{3}+102 \ln \relax (2)^{2} \left (x -\ln \relax (2)\right )+\frac {187 \ln \relax (2) \left (x -\ln \relax (2)\right )^{2}}{2}+\frac {28 \ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )^{2}}{3}+112 \ln \relax (2) \left (x -\ln \relax (2)\right )-10 \ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )+\frac {4 \ln \relax (2)^{3} \left (\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )-x +\ln \relax (2)\right )}{3}+4 \ln \relax (2)^{2} \left (\frac {\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )^{2}}{2}-\frac {\left (x -\ln \relax (2)\right )^{2}}{4}\right )+4 \ln \relax (2) \left (\frac {\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )^{3}}{3}-\frac {\left (x -\ln \relax (2)\right )^{3}}{9}\right )+\frac {\ln \relax (2)^{4} \ln \left (x -\ln \relax (2)\right )}{3}+17 \ln \relax (2)^{2} \left (\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )-x +\ln \relax (2)\right )+34 \ln \relax (2) \left (\frac {\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )^{2}}{2}-\frac {\left (x -\ln \relax (2)\right )^{2}}{4}\right )+\frac {56 \ln \relax (2) \left (\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )-x +\ln \relax (2)\right )}{3}+\frac {17 \ln \relax (2)^{3} \ln \left (x -\ln \relax (2)\right )}{3}+\frac {85 \left (x -\ln \relax (2)\right )^{3}}{3}+\frac {5 \left (x -\ln \relax (2)\right )^{4}}{3}\)	\(401\)
default	\(-50 x +50 \ln \relax (2)+11 \ln \relax (2)^{2} \left (x -\ln \relax (2)\right )^{2}+\frac {140 \left (x -\ln \relax (2)\right )^{2}}{3}+\frac {28 \ln \relax (2)^{2} \ln \left (x -\ln \relax (2)\right )}{3}-10 \ln \relax (2) \ln \left (x -\ln \relax (2)\right )+\frac {\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )^{4}}{3}+8 \ln \relax (2)^{3} \left (x -\ln \relax (2)\right )+\frac {64 \ln \relax (2) \left (x -\ln \relax (2)\right )^{3}}{9}+\frac {17 \ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )^{3}}{3}+102 \ln \relax (2)^{2} \left (x -\ln \relax (2)\right )+\frac {187 \ln \relax (2) \left (x -\ln \relax (2)\right )^{2}}{2}+\frac {28 \ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )^{2}}{3}+112 \ln \relax (2) \left (x -\ln \relax (2)\right )-10 \ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )+\frac {4 \ln \relax (2)^{3} \left (\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )-x +\ln \relax (2)\right )}{3}+4 \ln \relax (2)^{2} \left (\frac {\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )^{2}}{2}-\frac {\left (x -\ln \relax (2)\right )^{2}}{4}\right )+4 \ln \relax (2) \left (\frac {\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )^{3}}{3}-\frac {\left (x -\ln \relax (2)\right )^{3}}{9}\right )+\frac {\ln \relax (2)^{4} \ln \left (x -\ln \relax (2)\right )}{3}+17 \ln \relax (2)^{2} \left (\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )-x +\ln \relax (2)\right )+34 \ln \relax (2) \left (\frac {\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )^{2}}{2}-\frac {\left (x -\ln \relax (2)\right )^{2}}{4}\right )+\frac {56 \ln \relax (2) \left (\ln \left (x -\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )-x +\ln \relax (2)\right )}{3}+\frac {17 \ln \relax (2)^{3} \ln \left (x -\ln \relax (2)\right )}{3}+\frac {85 \left (x -\ln \relax (2)\right )^{3}}{3}+\frac {5 \left (x -\ln \relax (2)\right )^{4}}{3}\)	\(401\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((4*x^3+51*x^2+56*x-30)*ln(2)-4*x^4-51*x^3-56*x^2+30*x)*ln(x-ln(2))+(20*x^3+255*x^2+280*x-150)*ln(2)-21*x
^4-272*x^3-308*x^2+180*x)/(3*ln(2)-3*x),x,method=_RETURNVERBOSE)

[Out]

(1/3*x^4+17/3*x^3+28/3*x^2-10*x)*ln(x-ln(2))+5/3*x^4+85/3*x^3+140/3*x^2-50*x

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maxima [B]  time = 0.48, size = 606, normalized size = 23.31 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^3+51*x^2+56*x-30)*log(2)-4*x^4-51*x^3-56*x^2+30*x)*log(x-log(2))+(20*x^3+255*x^2+280*x-150)*l
og(2)-21*x^4-272*x^3-308*x^2+180*x)/(3*log(2)-3*x),x, algorithm="maxima")

[Out]

-2/3*log(2)^4*log(x - log(2))^2 + 38/9*log(2)^4*log(x - log(2)) - 17/2*log(2)^3*log(x - log(2))^2 + 5/3*x^4 +
56/27*x^3*log(2) + 25/9*x^2*log(2)^2 + 38/9*x*log(2)^3 + 119/2*log(2)^3*log(x - log(2)) - 28/3*log(2)^2*log(x
- log(2))^2 + 85/3*x^3 + 153/4*x^2*log(2) + 119/2*x*log(2)^2 - 2/9*(6*log(2)^3*log(x - log(2)) + 2*x^3 + 3*x^2
*log(2) + 6*x*log(2)^2)*log(2)*log(x - log(2)) - 17/2*(2*log(2)^2*log(x - log(2)) + x^2 + 2*x*log(2))*log(2)*l
og(x - log(2)) - 56/3*(log(2)*log(x - log(2)) + x)*log(2)*log(x - log(2)) + 224/3*log(2)^2*log(x - log(2)) + 1
0*log(2)*log(x - log(2))^2 + 140/3*x^2 + 1/27*(18*log(2)^3*log(x - log(2))^2 + 66*log(2)^3*log(x - log(2)) + 4
*x^3 + 15*x^2*log(2) + 66*x*log(2)^2)*log(2) - 10/9*(6*log(2)^3*log(x - log(2)) + 2*x^3 + 3*x^2*log(2) + 6*x*l
og(2)^2)*log(2) + 17/4*(2*log(2)^2*log(x - log(2))^2 + 6*log(2)^2*log(x - log(2)) + x^2 + 6*x*log(2))*log(2) -
85/2*(2*log(2)^2*log(x - log(2)) + x^2 + 2*x*log(2))*log(2) + 28/3*(log(2)*log(x - log(2))^2 + 2*log(2)*log(x
- log(2)) + 2*x)*log(2) - 280/3*(log(2)*log(x - log(2)) + x)*log(2) + 224/3*x*log(2) + 1/9*(12*log(2)^4*log(x
- log(2)) + 3*x^4 + 4*x^3*log(2) + 6*x^2*log(2)^2 + 12*x*log(2)^3)*log(x - log(2)) + 17/6*(6*log(2)^3*log(x -
log(2)) + 2*x^3 + 3*x^2*log(2) + 6*x*log(2)^2)*log(x - log(2)) + 28/3*(2*log(2)^2*log(x - log(2)) + x^2 + 2*x
*log(2))*log(x - log(2)) - 10*(log(2)*log(x - log(2)) + x)*log(x - log(2)) - 50*x

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mupad [B]  time = 5.26, size = 400, normalized size = 15.38 \begin {gather*} \frac {7\,x^2\,{\ln \relax (2)}^2}{2}-60\,x-\ln \left (x-\ln \relax (2)\right )\,\left (\frac {280\,{\ln \relax (2)}^2}{3}-50\,\ln \relax (2)+85\,{\ln \relax (2)}^3+\frac {20\,{\ln \relax (2)}^4}{3}\right )-x\,\left (\frac {280\,\ln \relax (2)}{3}+\ln \relax (2)\,\left (85\,\ln \relax (2)+\frac {20\,{\ln \relax (2)}^2}{3}\right )\right )+\frac {308\,\ln \left (x-\ln \relax (2)\right )\,{\ln \relax (2)}^2}{3}+\frac {272\,\ln \left (x-\ln \relax (2)\right )\,{\ln \relax (2)}^3}{3}+7\,\ln \left (x-\ln \relax (2)\right )\,{\ln \relax (2)}^4+\frac {308\,x\,\ln \relax (2)}{3}-x^2\,\left (\frac {85\,\ln \relax (2)}{2}+\frac {10\,{\ln \relax (2)}^2}{3}\right )+\frac {272\,x\,{\ln \relax (2)}^2}{3}+\frac {136\,x^2\,\ln \relax (2)}{3}+7\,x\,{\ln \relax (2)}^3+\frac {x^3\,\ln \relax (2)}{9}+\frac {154\,x^2}{3}+\frac {272\,x^3}{9}+\frac {7\,x^4}{4}-60\,\ln \left (x-\ln \relax (2)\right )\,\ln \relax (2)-\frac {x^4\,\left (\frac {\ln \relax (2)}{12}+\frac {17}{3}\right )-x^5\,\ln \left (x-\ln \relax (2)\right )-\ln \left (x-\ln \relax (2)\right )\,\left (28\,{\ln \relax (2)}^3-30\,{\ln \relax (2)}^2+17\,{\ln \relax (2)}^4+{\ln \relax (2)}^5\right )+x^3\,\left (\frac {17\,\ln \relax (2)}{6}+\frac {{\ln \relax (2)}^2}{6}+14\right )+x^2\,\left (14\,\ln \relax (2)+\frac {17\,{\ln \relax (2)}^2}{2}+\frac {{\ln \relax (2)}^3}{2}-30\right )+\frac {x^5}{4}+x^4\,\ln \left (x-\ln \relax (2)\right )\,\left (\ln \relax (2)-17\right )+x\,\ln \left (x-\ln \relax (2)\right )\,\left (28\,{\ln \relax (2)}^2-60\,\ln \relax (2)+17\,{\ln \relax (2)}^3+{\ln \relax (2)}^4\right )-\frac {x\,\left (28\,{\ln \relax (2)}^3-30\,{\ln \relax (2)}^2+17\,{\ln \relax (2)}^4+{\ln \relax (2)}^5\right )}{\ln \relax (2)}+x^3\,\ln \left (x-\ln \relax (2)\right )\,\left (17\,\ln \relax (2)-28\right )+x^2\,\ln \left (x-\ln \relax (2)\right )\,\left (28\,\ln \relax (2)+30\right )}{3\,x-3\,\ln \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x - log(2))*(56*x^2 - log(2)*(56*x + 51*x^2 + 4*x^3 - 30) - 30*x + 51*x^3 + 4*x^4) - log(2)*(280*x +
255*x^2 + 20*x^3 - 150) - 180*x + 308*x^2 + 272*x^3 + 21*x^4)/(3*x - 3*log(2)),x)

[Out]

(7*x^2*log(2)^2)/2 - 60*x - log(x - log(2))*((280*log(2)^2)/3 - 50*log(2) + 85*log(2)^3 + (20*log(2)^4)/3) - x
*((280*log(2))/3 + log(2)*(85*log(2) + (20*log(2)^2)/3)) + (308*log(x - log(2))*log(2)^2)/3 + (272*log(x - log
(2))*log(2)^3)/3 + 7*log(x - log(2))*log(2)^4 + (308*x*log(2))/3 - x^2*((85*log(2))/2 + (10*log(2)^2)/3) + (27
2*x*log(2)^2)/3 + (136*x^2*log(2))/3 + 7*x*log(2)^3 + (x^3*log(2))/9 + (154*x^2)/3 + (272*x^3)/9 + (7*x^4)/4 -
60*log(x - log(2))*log(2) - (x^4*(log(2)/12 + 17/3) - x^5*log(x - log(2)) - log(x - log(2))*(28*log(2)^3 - 30
*log(2)^2 + 17*log(2)^4 + log(2)^5) + x^3*((17*log(2))/6 + log(2)^2/6 + 14) + x^2*(14*log(2) + (17*log(2)^2)/2
+ log(2)^3/2 - 30) + x^5/4 + x^4*log(x - log(2))*(log(2) - 17) + x*log(x - log(2))*(28*log(2)^2 - 60*log(2) +
17*log(2)^3 + log(2)^4) - (x*(28*log(2)^3 - 30*log(2)^2 + 17*log(2)^4 + log(2)^5))/log(2) + x^3*log(x - log(2
))*(17*log(2) - 28) + x^2*log(x - log(2))*(28*log(2) + 30))/(3*x - 3*log(2))

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sympy [B]  time = 0.20, size = 51, normalized size = 1.96 \begin {gather*} \frac {5 x^{4}}{3} + \frac {85 x^{3}}{3} + \frac {140 x^{2}}{3} - 50 x + \left (\frac {x^{4}}{3} + \frac {17 x^{3}}{3} + \frac {28 x^{2}}{3} - 10 x\right ) \log {\left (x - \log {\relax (2 )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x**3+51*x**2+56*x-30)*ln(2)-4*x**4-51*x**3-56*x**2+30*x)*ln(x-ln(2))+(20*x**3+255*x**2+280*x-15
0)*ln(2)-21*x**4-272*x**3-308*x**2+180*x)/(3*ln(2)-3*x),x)

[Out]

5*x**4/3 + 85*x**3/3 + 140*x**2/3 - 50*x + (x**4/3 + 17*x**3/3 + 28*x**2/3 - 10*x)*log(x - log(2))

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