\(\int \frac {(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx\) [1290]

Optimal result

Integrand size = 22, antiderivative size = 65 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx=\frac {8333293 x}{390625}+\frac {5555569 x^2}{156250}-\frac {422841 x^3}{15625}-\frac {1677159 x^4}{12500}-\frac {228447 x^5}{3125}+\frac {35883 x^6}{250}+\frac {34992 x^7}{175}+\frac {729 x^8}{10}+\frac {121 \log (3+5 x)}{1953125} \]

[Out]

8333293/390625*x+5555569/156250*x^2-422841/15625*x^3-1677159/12500*x^4-228447/3125*x^5+35883/250*x^6+34992/175
*x^7+729/10*x^8+121/1953125*ln(3+5*x)

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx=\frac {729 x^8}{10}+\frac {34992 x^7}{175}+\frac {35883 x^6}{250}-\frac {228447 x^5}{3125}-\frac {1677159 x^4}{12500}-\frac {422841 x^3}{15625}+\frac {5555569 x^2}{156250}+\frac {8333293 x}{390625}+\frac {121 \log (5 x+3)}{1953125} \]

[In]

Int[((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x),x]

[Out]

(8333293*x)/390625 + (5555569*x^2)/156250 - (422841*x^3)/15625 - (1677159*x^4)/12500 - (228447*x^5)/3125 + (35
883*x^6)/250 + (34992*x^7)/175 + (729*x^8)/10 + (121*Log[3 + 5*x])/1953125

Rule 90

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {8333293}{390625}+\frac {5555569 x}{78125}-\frac {1268523 x^2}{15625}-\frac {1677159 x^3}{3125}-\frac {228447 x^4}{625}+\frac {107649 x^5}{125}+\frac {34992 x^6}{25}+\frac {2916 x^7}{5}+\frac {121}{390625 (3+5 x)}\right ) \, dx \\ & = \frac {8333293 x}{390625}+\frac {5555569 x^2}{156250}-\frac {422841 x^3}{15625}-\frac {1677159 x^4}{12500}-\frac {228447 x^5}{3125}+\frac {35883 x^6}{250}+\frac {34992 x^7}{175}+\frac {729 x^8}{10}+\frac {121 \log (3+5 x)}{1953125} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.80 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx=\frac {966660747+5833305100 x+9722245750 x^2-7399717500 x^3-36687853125 x^4-19989112500 x^5+39247031250 x^6+54675000000 x^7+19933593750 x^8+16940 \log (3+5 x)}{273437500} \]

[In]

Integrate[((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x),x]

[Out]

(966660747 + 5833305100*x + 9722245750*x^2 - 7399717500*x^3 - 36687853125*x^4 - 19989112500*x^5 + 39247031250*
x^6 + 54675000000*x^7 + 19933593750*x^8 + 16940*Log[3 + 5*x])/273437500

Maple [A] (verified)

Time = 0.80 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.71

method	result	size
parallelrisch	\(\frac {729 x^{8}}{10}+\frac {34992 x^{7}}{175}+\frac {35883 x^{6}}{250}-\frac {228447 x^{5}}{3125}-\frac {1677159 x^{4}}{12500}-\frac {422841 x^{3}}{15625}+\frac {5555569 x^{2}}{156250}+\frac {8333293 x}{390625}+\frac {121 \ln \left (x +\frac {3}{5}\right )}{1953125}\)	\(46\)
default	\(\frac {8333293 x}{390625}+\frac {5555569 x^{2}}{156250}-\frac {422841 x^{3}}{15625}-\frac {1677159 x^{4}}{12500}-\frac {228447 x^{5}}{3125}+\frac {35883 x^{6}}{250}+\frac {34992 x^{7}}{175}+\frac {729 x^{8}}{10}+\frac {121 \ln \left (3+5 x \right )}{1953125}\)	\(48\)
norman	\(\frac {8333293 x}{390625}+\frac {5555569 x^{2}}{156250}-\frac {422841 x^{3}}{15625}-\frac {1677159 x^{4}}{12500}-\frac {228447 x^{5}}{3125}+\frac {35883 x^{6}}{250}+\frac {34992 x^{7}}{175}+\frac {729 x^{8}}{10}+\frac {121 \ln \left (3+5 x \right )}{1953125}\)	\(48\)
risch	\(\frac {8333293 x}{390625}+\frac {5555569 x^{2}}{156250}-\frac {422841 x^{3}}{15625}-\frac {1677159 x^{4}}{12500}-\frac {228447 x^{5}}{3125}+\frac {35883 x^{6}}{250}+\frac {34992 x^{7}}{175}+\frac {729 x^{8}}{10}+\frac {121 \ln \left (3+5 x \right )}{1953125}\)	\(48\)
meijerg	\(\frac {121 \ln \left (1+\frac {5 x}{3}\right )}{1953125}+64 x -\frac {56 x \left (-5 x +6\right )}{25}-\frac {1512 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{125}+\frac {1701 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{625}+\frac {5103 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{15625}-\frac {19683 x \left (-\frac {218750}{243} x^{5}+\frac {17500}{27} x^{4}-\frac {4375}{9} x^{3}+\frac {3500}{9} x^{2}-350 x +420\right )}{62500}+\frac {531441 x \left (\frac {625000}{243} x^{6}-\frac {437500}{243} x^{5}+\frac {35000}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{9} x^{2}-700 x +840\right )}{5468750}-\frac {177147 x \left (-\frac {2734375}{243} x^{7}+\frac {625000}{81} x^{6}-\frac {437500}{81} x^{5}+\frac {35000}{9} x^{4}-\frac {8750}{3} x^{3}+\frac {7000}{3} x^{2}-2100 x +2520\right )}{27343750}\)	\(174\)

[In]

int((1-2*x)^2*(2+3*x)^6/(3+5*x),x,method=_RETURNVERBOSE)

[Out]

729/10*x^8+34992/175*x^7+35883/250*x^6-228447/3125*x^5-1677159/12500*x^4-422841/15625*x^3+5555569/156250*x^2+8
333293/390625*x+121/1953125*ln(x+3/5)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.72 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx=\frac {729}{10} \, x^{8} + \frac {34992}{175} \, x^{7} + \frac {35883}{250} \, x^{6} - \frac {228447}{3125} \, x^{5} - \frac {1677159}{12500} \, x^{4} - \frac {422841}{15625} \, x^{3} + \frac {5555569}{156250} \, x^{2} + \frac {8333293}{390625} \, x + \frac {121}{1953125} \, \log \left (5 \, x + 3\right ) \]

[In]

integrate((1-2*x)^2*(2+3*x)^6/(3+5*x),x, algorithm="fricas")

[Out]

729/10*x^8 + 34992/175*x^7 + 35883/250*x^6 - 228447/3125*x^5 - 1677159/12500*x^4 - 422841/15625*x^3 + 5555569/
156250*x^2 + 8333293/390625*x + 121/1953125*log(5*x + 3)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.94 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx=\frac {729 x^{8}}{10} + \frac {34992 x^{7}}{175} + \frac {35883 x^{6}}{250} - \frac {228447 x^{5}}{3125} - \frac {1677159 x^{4}}{12500} - \frac {422841 x^{3}}{15625} + \frac {5555569 x^{2}}{156250} + \frac {8333293 x}{390625} + \frac {121 \log {\left (5 x + 3 \right )}}{1953125} \]

[In]

integrate((1-2*x)**2*(2+3*x)**6/(3+5*x),x)

[Out]

729*x**8/10 + 34992*x**7/175 + 35883*x**6/250 - 228447*x**5/3125 - 1677159*x**4/12500 - 422841*x**3/15625 + 55
55569*x**2/156250 + 8333293*x/390625 + 121*log(5*x + 3)/1953125

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.72 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx=\frac {729}{10} \, x^{8} + \frac {34992}{175} \, x^{7} + \frac {35883}{250} \, x^{6} - \frac {228447}{3125} \, x^{5} - \frac {1677159}{12500} \, x^{4} - \frac {422841}{15625} \, x^{3} + \frac {5555569}{156250} \, x^{2} + \frac {8333293}{390625} \, x + \frac {121}{1953125} \, \log \left (5 \, x + 3\right ) \]

[In]

integrate((1-2*x)^2*(2+3*x)^6/(3+5*x),x, algorithm="maxima")

[Out]

729/10*x^8 + 34992/175*x^7 + 35883/250*x^6 - 228447/3125*x^5 - 1677159/12500*x^4 - 422841/15625*x^3 + 5555569/
156250*x^2 + 8333293/390625*x + 121/1953125*log(5*x + 3)

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.74 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx=\frac {729}{10} \, x^{8} + \frac {34992}{175} \, x^{7} + \frac {35883}{250} \, x^{6} - \frac {228447}{3125} \, x^{5} - \frac {1677159}{12500} \, x^{4} - \frac {422841}{15625} \, x^{3} + \frac {5555569}{156250} \, x^{2} + \frac {8333293}{390625} \, x + \frac {121}{1953125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]

[In]

integrate((1-2*x)^2*(2+3*x)^6/(3+5*x),x, algorithm="giac")

[Out]

729/10*x^8 + 34992/175*x^7 + 35883/250*x^6 - 228447/3125*x^5 - 1677159/12500*x^4 - 422841/15625*x^3 + 5555569/
156250*x^2 + 8333293/390625*x + 121/1953125*log(abs(5*x + 3))

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.69 \[ \int \frac {(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx=\frac {8333293\,x}{390625}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{1953125}+\frac {5555569\,x^2}{156250}-\frac {422841\,x^3}{15625}-\frac {1677159\,x^4}{12500}-\frac {228447\,x^5}{3125}+\frac {35883\,x^6}{250}+\frac {34992\,x^7}{175}+\frac {729\,x^8}{10} \]

[In]

int(((2*x - 1)^2*(3*x + 2)^6)/(5*x + 3),x)

[Out]

(8333293*x)/390625 + (121*log(x + 3/5))/1953125 + (5555569*x^2)/156250 - (422841*x^3)/15625 - (1677159*x^4)/12
500 - (228447*x^5)/3125 + (35883*x^6)/250 + (34992*x^7)/175 + (729*x^8)/10