\(\int \frac {(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx\) [1291]

Optimal result

Integrand size = 22, antiderivative size = 58 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx=\frac {833293 x}{78125}+\frac {305569 x^2}{31250}-\frac {72841 x^3}{3125}-\frac {102159 x^4}{2500}+\frac {7803 x^5}{625}+\frac {1404 x^6}{25}+\frac {972 x^7}{35}+\frac {121 \log (3+5 x)}{390625} \]

[Out]

833293/78125*x+305569/31250*x^2-72841/3125*x^3-102159/2500*x^4+7803/625*x^5+1404/25*x^6+972/35*x^7+121/390625*
ln(3+5*x)

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 58, 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} \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx=\frac {972 x^7}{35}+\frac {1404 x^6}{25}+\frac {7803 x^5}{625}-\frac {102159 x^4}{2500}-\frac {72841 x^3}{3125}+\frac {305569 x^2}{31250}+\frac {833293 x}{78125}+\frac {121 \log (5 x+3)}{390625} \]

[In]

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

[Out]

(833293*x)/78125 + (305569*x^2)/31250 - (72841*x^3)/3125 - (102159*x^4)/2500 + (7803*x^5)/625 + (1404*x^6)/25
+ (972*x^7)/35 + (121*Log[3 + 5*x])/390625

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 {833293}{78125}+\frac {305569 x}{15625}-\frac {218523 x^2}{3125}-\frac {102159 x^3}{625}+\frac {7803 x^4}{125}+\frac {8424 x^5}{25}+\frac {972 x^6}{5}+\frac {121}{78125 (3+5 x)}\right ) \, dx \\ & = \frac {833293 x}{78125}+\frac {305569 x^2}{31250}-\frac {72841 x^3}{3125}-\frac {102159 x^4}{2500}+\frac {7803 x^5}{625}+\frac {1404 x^6}{25}+\frac {972 x^7}{35}+\frac {121 \log (3+5 x)}{390625} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.81 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx=\frac {124071027+583305100 x+534745750 x^2-1274717500 x^3-2234728125 x^4+682762500 x^5+3071250000 x^6+1518750000 x^7+16940 \log (3+5 x)}{54687500} \]

[In]

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

[Out]

(124071027 + 583305100*x + 534745750*x^2 - 1274717500*x^3 - 2234728125*x^4 + 682762500*x^5 + 3071250000*x^6 +
1518750000*x^7 + 16940*Log[3 + 5*x])/54687500

Maple [A] (verified)

Time = 0.77 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.71

method	result	size
parallelrisch	\(\frac {972 x^{7}}{35}+\frac {1404 x^{6}}{25}+\frac {7803 x^{5}}{625}-\frac {102159 x^{4}}{2500}-\frac {72841 x^{3}}{3125}+\frac {305569 x^{2}}{31250}+\frac {833293 x}{78125}+\frac {121 \ln \left (x +\frac {3}{5}\right )}{390625}\)	\(41\)
default	\(\frac {833293 x}{78125}+\frac {305569 x^{2}}{31250}-\frac {72841 x^{3}}{3125}-\frac {102159 x^{4}}{2500}+\frac {7803 x^{5}}{625}+\frac {1404 x^{6}}{25}+\frac {972 x^{7}}{35}+\frac {121 \ln \left (3+5 x \right )}{390625}\)	\(43\)
norman	\(\frac {833293 x}{78125}+\frac {305569 x^{2}}{31250}-\frac {72841 x^{3}}{3125}-\frac {102159 x^{4}}{2500}+\frac {7803 x^{5}}{625}+\frac {1404 x^{6}}{25}+\frac {972 x^{7}}{35}+\frac {121 \ln \left (3+5 x \right )}{390625}\)	\(43\)
risch	\(\frac {833293 x}{78125}+\frac {305569 x^{2}}{31250}-\frac {72841 x^{3}}{3125}-\frac {102159 x^{4}}{2500}+\frac {7803 x^{5}}{625}+\frac {1404 x^{6}}{25}+\frac {972 x^{7}}{35}+\frac {121 \ln \left (3+5 x \right )}{390625}\)	\(43\)
meijerg	\(\frac {121 \ln \left (1+\frac {5 x}{3}\right )}{390625}+\frac {112 x}{5}+\frac {56 x \left (-5 x +6\right )}{25}-\frac {126 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{25}+\frac {567 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{1250}+\frac {35721 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{62500}-\frac {6561 x \left (-\frac {218750}{243} x^{5}+\frac {17500}{27} x^{4}-\frac {4375}{9} x^{3}+\frac {3500}{9} x^{2}-350 x +420\right )}{78125}+\frac {59049 x \left (\frac {625000}{243} x^{6}-\frac {437500}{243} x^{5}+\frac {35000}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{9} x^{2}-700 x +840\right )}{5468750}\)	\(136\)

[In]

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

[Out]

972/35*x^7+1404/25*x^6+7803/625*x^5-102159/2500*x^4-72841/3125*x^3+305569/31250*x^2+833293/78125*x+121/390625*
ln(x+3/5)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.72 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx=\frac {972}{35} \, x^{7} + \frac {1404}{25} \, x^{6} + \frac {7803}{625} \, x^{5} - \frac {102159}{2500} \, x^{4} - \frac {72841}{3125} \, x^{3} + \frac {305569}{31250} \, x^{2} + \frac {833293}{78125} \, x + \frac {121}{390625} \, \log \left (5 \, x + 3\right ) \]

[In]

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

[Out]

972/35*x^7 + 1404/25*x^6 + 7803/625*x^5 - 102159/2500*x^4 - 72841/3125*x^3 + 305569/31250*x^2 + 833293/78125*x
+ 121/390625*log(5*x + 3)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.93 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx=\frac {972 x^{7}}{35} + \frac {1404 x^{6}}{25} + \frac {7803 x^{5}}{625} - \frac {102159 x^{4}}{2500} - \frac {72841 x^{3}}{3125} + \frac {305569 x^{2}}{31250} + \frac {833293 x}{78125} + \frac {121 \log {\left (5 x + 3 \right )}}{390625} \]

[In]

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

[Out]

972*x**7/35 + 1404*x**6/25 + 7803*x**5/625 - 102159*x**4/2500 - 72841*x**3/3125 + 305569*x**2/31250 + 833293*x
/78125 + 121*log(5*x + 3)/390625

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.72 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx=\frac {972}{35} \, x^{7} + \frac {1404}{25} \, x^{6} + \frac {7803}{625} \, x^{5} - \frac {102159}{2500} \, x^{4} - \frac {72841}{3125} \, x^{3} + \frac {305569}{31250} \, x^{2} + \frac {833293}{78125} \, x + \frac {121}{390625} \, \log \left (5 \, x + 3\right ) \]

[In]

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

[Out]

972/35*x^7 + 1404/25*x^6 + 7803/625*x^5 - 102159/2500*x^4 - 72841/3125*x^3 + 305569/31250*x^2 + 833293/78125*x
+ 121/390625*log(5*x + 3)

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 43, normalized size of antiderivative = 0.74 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx=\frac {972}{35} \, x^{7} + \frac {1404}{25} \, x^{6} + \frac {7803}{625} \, x^{5} - \frac {102159}{2500} \, x^{4} - \frac {72841}{3125} \, x^{3} + \frac {305569}{31250} \, x^{2} + \frac {833293}{78125} \, x + \frac {121}{390625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]

[In]

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

[Out]

972/35*x^7 + 1404/25*x^6 + 7803/625*x^5 - 102159/2500*x^4 - 72841/3125*x^3 + 305569/31250*x^2 + 833293/78125*x
+ 121/390625*log(abs(5*x + 3))

Mupad [B] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.69 \[ \int \frac {(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx=\frac {833293\,x}{78125}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{390625}+\frac {305569\,x^2}{31250}-\frac {72841\,x^3}{3125}-\frac {102159\,x^4}{2500}+\frac {7803\,x^5}{625}+\frac {1404\,x^6}{25}+\frac {972\,x^7}{35} \]

[In]

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

[Out]

(833293*x)/78125 + (121*log(x + 3/5))/390625 + (305569*x^2)/31250 - (72841*x^3)/3125 - (102159*x^4)/2500 + (78
03*x^5)/625 + (1404*x^6)/25 + (972*x^7)/35