3.1322 \(\int \frac {(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx\)

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

[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]  time = 0.04, antiderivative size = 80, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ \frac {8748 x^7}{875}+\frac {13608 x^6}{625}+\frac {104247 x^5}{15625}-\frac {193833 x^4}{12500}-\frac {162612 x^3}{15625}+\frac {1390203 x^2}{390625}+\frac {9251661 x}{1953125}-\frac {2497}{9765625 (5 x+3)}-\frac {121}{19531250 (5 x+3)^2}+\frac {21949 \log (5 x+3)}{9765625} \]

Antiderivative was successfully verified.

[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 88

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*} \int \frac {(1-2 x)^2 (2+3 x)^7}{(3+5 x)^3} \, dx &=\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]  time = 0.04, size = 71, normalized size = 0.89 \[ \frac {341718750000 x^9+1154250000000 x^8+1244084062500 x^7+11543765625 x^6-909633768750 x^5-496018096875 x^4+179818432500 x^3+275860261575 x^2+103624499690 x+3072860 (5 x+3)^2 \log (5 x+3)[phone]}{1367187500 (5 x+3)^2} \]

Antiderivative was successfully verified.

[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)

________________________________________________________________________________________

fricas [A]  time = 0.53, size = 77, normalized size = 0.96 \[ \frac {68343750000 \, x^{9} + 230850000000 \, x^{8} + 248816812500 \, x^{7} + 2308753125 \, x^{6} - 181926753750 \, x^{5} - 99203619375 \, x^{4} + 35963686500 \, x^{3} + 47615255100 \, x^{2} + 614572 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 11656743280 \, x - 211442}{273437500 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[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)

________________________________________________________________________________________

giac [A]  time = 1.03, size = 57, normalized size = 0.71 \[ \frac {8748}{875} \, x^{7} + \frac {13608}{625} \, x^{6} + \frac {104247}{15625} \, x^{5} - \frac {193833}{12500} \, x^{4} - \frac {162612}{15625} \, x^{3} + \frac {1390203}{390625} \, x^{2} + \frac {9251661}{1953125} \, x - \frac {11 \, {\left (2270 \, x + 1373\right )}}{19531250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {21949}{9765625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[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))

________________________________________________________________________________________

maple [A]  time = 0.01, size = 61, normalized size = 0.76 \[ \frac {8748 x^{7}}{875}+\frac {13608 x^{6}}{625}+\frac {104247 x^{5}}{15625}-\frac {193833 x^{4}}{12500}-\frac {162612 x^{3}}{15625}+\frac {1390203 x^{2}}{390625}+\frac {9251661 x}{1953125}+\frac {21949 \ln \left (5 x +3\right )}{9765625}-\frac {121}{19531250 \left (5 x +3\right )^{2}}-\frac {2497}{9765625 \left (5 x +3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[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/(5*x+3)^2-2497/9765625/(5*x+3)+21949/9765625*ln(5*x+3)

________________________________________________________________________________________

maxima [A]  time = 0.63, size = 61, normalized size = 0.76 \[ \frac {8748}{875} \, x^{7} + \frac {13608}{625} \, x^{6} + \frac {104247}{15625} \, x^{5} - \frac {193833}{12500} \, x^{4} - \frac {162612}{15625} \, x^{3} + \frac {1390203}{390625} \, x^{2} + \frac {9251661}{1953125} \, x - \frac {11 \, {\left (2270 \, x + 1373\right )}}{19531250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {21949}{9765625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[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)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[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

________________________________________________________________________________________

sympy [A]  time = 0.15, size = 71, normalized size = 0.89 \[ \frac {8748 x^{7}}{875} + \frac {13608 x^{6}}{625} + \frac {104247 x^{5}}{15625} - \frac {193833 x^{4}}{12500} - \frac {162612 x^{3}}{15625} + \frac {1390203 x^{2}}{390625} + \frac {9251661 x}{1953125} + \frac {- 24970 x - 15103}{488281250 x^{2} + 585937500 x + 175781250} + \frac {21949 \log {\left (5 x + 3 \right )}}{9765625} \]

Verification of antiderivative is not currently implemented for this CAS.

[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

________________________________________________________________________________________