\(\int \frac {(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx\) [1322]

Optimal result

Integrand size = 22, antiderivative size = 80 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx=\frac {9251661 x}{1953125}+\frac {1390203 x^2}{390625}-\frac {162612 x^3}{15625}-\frac {193833 x^4}{12500}+\frac {104247 x^5}{15625}+\frac {13608 x^6}{625}+\frac {8748 x^7}{875}-\frac {121}{19531250 (3+5 x)^2}-\frac {2497}{9765625 (3+5 x)}+\frac {21949 \log (3+5 x)}{9765625} \]

[Out]

9251661/1953125*x+1390203/390625*x^2-162612/15625*x^3-193833/12500*x^4+104247/15625*x^5+13608/625*x^6+8748/875
*x^7-121/19531250/(3+5*x)^2-2497/9765625/(3+5*x)+21949/9765625*ln(3+5*x)

Rubi [A] (verified)

Time = 0.03 (sec) , antiderivative size = 80, 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} \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx=\frac {8748 x^7}{875}+\frac {13608 x^6}{625}+\frac {104247 x^5}{15625}-\frac {193833 x^4}{12500}-\frac {162612 x^3}{15625}+\frac {1390203 x^2}{390625}+\frac {9251661 x}{1953125}-\frac {2497}{9765625 (5 x+3)}-\frac {121}{19531250 (5 x+3)^2}+\frac {21949 \log (5 x+3)}{9765625} \]

[In]

Int[((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x)^3,x]

[Out]

(9251661*x)/1953125 + (1390203*x^2)/390625 - (162612*x^3)/15625 - (193833*x^4)/12500 + (104247*x^5)/15625 + (1
3608*x^6)/625 + (8748*x^7)/875 - 121/(19531250*(3 + 5*x)^2) - 2497/(9765625*(3 + 5*x)) + (21949*Log[3 + 5*x])/
9765625

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 {9251661}{1953125}+\frac {2780406 x}{390625}-\frac {487836 x^2}{15625}-\frac {193833 x^3}{3125}+\frac {104247 x^4}{3125}+\frac {81648 x^5}{625}+\frac {8748 x^6}{125}+\frac {121}{1953125 (3+5 x)^3}+\frac {2497}{1953125 (3+5 x)^2}+\frac {21949}{1953125 (3+5 x)}\right ) \, dx \\ & = \frac {9251661 x}{1953125}+\frac {1390203 x^2}{390625}-\frac {162612 x^3}{15625}-\frac {193833 x^4}{12500}+\frac {104247 x^5}{15625}+\frac {13608 x^6}{625}+\frac {8748 x^7}{875}-\frac {121}{19531250 (3+5 x)^2}-\frac {2497}{9765625 (3+5 x)}+\frac {21949 \log (3+5 x)}{9765625} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 71, normalized size of antiderivative = 0.89 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx=\frac {13601177777+103624499690 x+275860261575 x^2+179818432500 x^3-496018096875 x^4-909633768750 x^5+11543765625 x^6+1244084062500 x^7+1154250000000 x^8+341718750000 x^9+3072860 (3+5 x)^2 \log (3+5 x)}{1367187500 (3+5 x)^2} \]

[In]

Integrate[((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x)^3,x]

[Out]

(13601177777 + 103624499690*x + 275860261575*x^2 + 179818432500*x^3 - 496018096875*x^4 - 909633768750*x^5 + 11
543765625*x^6 + 1244084062500*x^7 + 1154250000000*x^8 + 341718750000*x^9 + 3072860*(3 + 5*x)^2*Log[3 + 5*x])/(
1367187500*(3 + 5*x)^2)

Maple [A] (verified)

Time = 0.78 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.71

method	result	size
risch	\(\frac {8748 x^{7}}{875}+\frac {13608 x^{6}}{625}+\frac {104247 x^{5}}{15625}-\frac {193833 x^{4}}{12500}-\frac {162612 x^{3}}{15625}+\frac {1390203 x^{2}}{390625}+\frac {9251661 x}{1953125}+\frac {-\frac {2497 x}{1953125}-\frac {15103}{19531250}}{\left (3+5 x \right )^{2}}+\frac {21949 \ln \left (3+5 x \right )}{9765625}\)	\(57\)
default	\(\frac {9251661 x}{1953125}+\frac {1390203 x^{2}}{390625}-\frac {162612 x^{3}}{15625}-\frac {193833 x^{4}}{12500}+\frac {104247 x^{5}}{15625}+\frac {13608 x^{6}}{625}+\frac {8748 x^{7}}{875}-\frac {121}{19531250 \left (3+5 x \right )^{2}}-\frac {2497}{9765625 \left (3+5 x \right )}+\frac {21949 \ln \left (3+5 x \right )}{9765625}\)	\(61\)
norman	\(\frac {\frac {249802459}{5859375} x +\frac {1224407377}{7031250} x^{2}+\frac {10275339}{78125} x^{3}-\frac {22675113}{62500} x^{4}-\frac {20791629}{31250} x^{5}+\frac {105543}{12500} x^{6}+\frac {3981069}{4375} x^{7}+\frac {147744}{175} x^{8}+\frac {8748}{35} x^{9}}{\left (3+5 x \right )^{2}}+\frac {21949 \ln \left (3+5 x \right )}{9765625}\)	\(62\)
parallelrisch	\(\frac {615093750000 x^{9}[phone] x^{8}[phone] x^{7}[phone] x^{6}-1637340783750 x^{5}-892832574375 x^{4}[phone] \ln \left (x +\frac {3}{5}\right ) x^{2}[phone] x^{3}[phone] \ln \left (x +\frac {3}{5}\right ) x [phone] x^{2}[phone] \ln \left (x +\frac {3}{5}\right )[phone] x}{2460937500 \left (3+5 x \right )^{2}}\)	\(76\)
meijerg	\(\frac {64 x \left (\frac {5 x}{3}+2\right )}{27 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {416 x^{2}}{27 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {592 x \left (15 x +6\right )}{225 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {21949 \ln \left (1+\frac {5 x}{3}\right )}{9765625}-\frac {924 x \left (\frac {100}{9} x^{2}+30 x +12\right )}{125 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {20412 x \left (-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {14742 x \left (\frac {1250}{81} x^{4}-\frac {625}{27} x^{3}+\frac {500}{9} x^{2}+150 x +60\right )}{3125 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {37179 x \left (-\frac {21875}{243} x^{5}+\frac {8750}{81} x^{4}-\frac {4375}{27} x^{3}+\frac {3500}{9} x^{2}+1050 x +420\right )}{31250 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {3483891 x \left (\frac {125000}{729} x^{6}-\frac {43750}{243} x^{5}+\frac {17500}{81} x^{4}-\frac {8750}{27} x^{3}+\frac {7000}{9} x^{2}+2100 x +840\right )}{3125000 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {433026 x \left (-\frac {390625}{729} x^{7}+\frac {125000}{243} x^{6}-\frac {43750}{81} x^{5}+\frac {17500}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{3} x^{2}+6300 x +2520\right )}{1953125 \left (1+\frac {5 x}{3}\right )^{2}}+\frac {3188646 x \left (\frac {3906250}{6561} x^{8}-\frac {390625}{729} x^{7}+\frac {125000}{243} x^{6}-\frac {43750}{81} x^{5}+\frac {17500}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{3} x^{2}+6300 x +2520\right )}{68359375 \left (1+\frac {5 x}{3}\right )^{2}}\)	\(297\)

[In]

int((1-2*x)^2*(2+3*x)^7/(3+5*x)^3,x,method=_RETURNVERBOSE)

[Out]

8748/875*x^7+13608/625*x^6+104247/15625*x^5-193833/12500*x^4-162612/15625*x^3+1390203/390625*x^2+9251661/19531
25*x+25*(-2497/48828125*x-15103/488281250)/(3+5*x)^2+21949/9765625*ln(3+5*x)

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 77, normalized size of antiderivative = 0.96 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx=\frac {68343750000 \, x^{9} + 230850000000 \, x^{8} + 248816812500 \, x^{7} + 2308753125 \, x^{6} - 181926753750 \, x^{5} - 99203619375 \, x^{4} + 35963686500 \, x^{3} + 47615255100 \, x^{2} + 614572 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 11656743280 \, x - 211442}{273437500 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

[In]

integrate((1-2*x)^2*(2+3*x)^7/(3+5*x)^3,x, algorithm="fricas")

[Out]

1/273437500*(68343750000*x^9 + 230850000000*x^8 + 248816812500*x^7 + 2308753125*x^6 - 181926753750*x^5 - 99203
619375*x^4 + 35963686500*x^3 + 47615255100*x^2 + 614572*(25*x^2 + 30*x + 9)*log(5*x + 3) + 11656743280*x - 211
442)/(25*x^2 + 30*x + 9)

Sympy [A] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 71, normalized size of antiderivative = 0.89 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx=\frac {8748 x^{7}}{875} + \frac {13608 x^{6}}{625} + \frac {104247 x^{5}}{15625} - \frac {193833 x^{4}}{12500} - \frac {162612 x^{3}}{15625} + \frac {1390203 x^{2}}{390625} + \frac {9251661 x}{1953125} + \frac {- 24970 x - 15103}{488281250 x^{2} + 585937500 x + 175781250} + \frac {21949 \log {\left (5 x + 3 \right )}}{9765625} \]

[In]

integrate((1-2*x)**2*(2+3*x)**7/(3+5*x)**3,x)

[Out]

8748*x**7/875 + 13608*x**6/625 + 104247*x**5/15625 - 193833*x**4/12500 - 162612*x**3/15625 + 1390203*x**2/3906
25 + 9251661*x/1953125 + (-24970*x - 15103)/(488281250*x**2 + 585937500*x + 175781250) + 21949*log(5*x + 3)/97
65625

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.76 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx=\frac {8748}{875} \, x^{7} + \frac {13608}{625} \, x^{6} + \frac {104247}{15625} \, x^{5} - \frac {193833}{12500} \, x^{4} - \frac {162612}{15625} \, x^{3} + \frac {1390203}{390625} \, x^{2} + \frac {9251661}{1953125} \, x - \frac {11 \, {\left (2270 \, x + 1373\right )}}{19531250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {21949}{9765625} \, \log \left (5 \, x + 3\right ) \]

[In]

integrate((1-2*x)^2*(2+3*x)^7/(3+5*x)^3,x, algorithm="maxima")

[Out]

8748/875*x^7 + 13608/625*x^6 + 104247/15625*x^5 - 193833/12500*x^4 - 162612/15625*x^3 + 1390203/390625*x^2 + 9
251661/1953125*x - 11/19531250*(2270*x + 1373)/(25*x^2 + 30*x + 9) + 21949/9765625*log(5*x + 3)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx=\frac {8748}{875} \, x^{7} + \frac {13608}{625} \, x^{6} + \frac {104247}{15625} \, x^{5} - \frac {193833}{12500} \, x^{4} - \frac {162612}{15625} \, x^{3} + \frac {1390203}{390625} \, x^{2} + \frac {9251661}{1953125} \, x - \frac {11 \, {\left (2270 \, x + 1373\right )}}{19531250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {21949}{9765625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]

[In]

integrate((1-2*x)^2*(2+3*x)^7/(3+5*x)^3,x, algorithm="giac")

[Out]

8748/875*x^7 + 13608/625*x^6 + 104247/15625*x^5 - 193833/12500*x^4 - 162612/15625*x^3 + 1390203/390625*x^2 + 9
251661/1953125*x - 11/19531250*(2270*x + 1373)/(5*x + 3)^2 + 21949/9765625*log(abs(5*x + 3))

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.71 \[ \int \frac {(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx=\frac {9251661\,x}{1953125}+\frac {21949\,\ln \left (x+\frac {3}{5}\right )}{9765625}-\frac {\frac {2497\,x}{48828125}+\frac {15103}{488281250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}+\frac {1390203\,x^2}{390625}-\frac {162612\,x^3}{15625}-\frac {193833\,x^4}{12500}+\frac {104247\,x^5}{15625}+\frac {13608\,x^6}{625}+\frac {8748\,x^7}{875} \]

[In]

int(((2*x - 1)^2*(3*x + 2)^7)/(5*x + 3)^3,x)

[Out]

(9251661*x)/1953125 + (21949*log(x + 3/5))/9765625 - ((2497*x)/48828125 + 15103/488281250)/((6*x)/5 + x^2 + 9/
25) + (1390203*x^2)/390625 - (162612*x^3)/15625 - (193833*x^4)/12500 + (104247*x^5)/15625 + (13608*x^6)/625 +
(8748*x^7)/875