3.1498 \(\int \frac{1}{(1-2 x) (2+3 x)^6 (3+5 x)^2} \, dx\)

Optimal. Leaf size=97 \[ -\frac{70752609}{16807 (3 x+2)}-\frac{15625}{11 (5 x+3)}-\frac{806121}{2401 (3 x+2)^2}-\frac{11457}{343 (3 x+2)^3}-\frac{162}{49 (3 x+2)^4}-\frac{9}{35 (3 x+2)^5}-\frac{128 \log (1-2 x)}{14235529}+\frac{2977686468 \log (3 x+2)}{117649}-\frac{3062500}{121} \log (5 x+3) \]

[Out]

-9/(35*(2 + 3*x)^5) - 162/(49*(2 + 3*x)^4) - 11457/(343*(2 + 3*x)^3) - 806121/(2
401*(2 + 3*x)^2) - 70752609/(16807*(2 + 3*x)) - 15625/(11*(3 + 5*x)) - (128*Log[
1 - 2*x])/14235529 + (2977686468*Log[2 + 3*x])/117649 - (3062500*Log[3 + 5*x])/1
21

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Rubi [A]  time = 0.111075, antiderivative size = 97, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{70752609}{16807 (3 x+2)}-\frac{15625}{11 (5 x+3)}-\frac{806121}{2401 (3 x+2)^2}-\frac{11457}{343 (3 x+2)^3}-\frac{162}{49 (3 x+2)^4}-\frac{9}{35 (3 x+2)^5}-\frac{128 \log (1-2 x)}{14235529}+\frac{2977686468 \log (3 x+2)}{117649}-\frac{3062500}{121} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-9/(35*(2 + 3*x)^5) - 162/(49*(2 + 3*x)^4) - 11457/(343*(2 + 3*x)^3) - 806121/(2
401*(2 + 3*x)^2) - 70752609/(16807*(2 + 3*x)) - 15625/(11*(3 + 5*x)) - (128*Log[
1 - 2*x])/14235529 + (2977686468*Log[2 + 3*x])/117649 - (3062500*Log[3 + 5*x])/1
21

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Rubi in Sympy [A]  time = 14.1825, size = 83, normalized size = 0.86 \[ - \frac{128 \log{\left (- 2 x + 1 \right )}}{14235529} + \frac{2977686468 \log{\left (3 x + 2 \right )}}{117649} - \frac{3062500 \log{\left (5 x + 3 \right )}}{121} - \frac{15625}{11 \left (5 x + 3\right )} - \frac{70752609}{16807 \left (3 x + 2\right )} - \frac{806121}{2401 \left (3 x + 2\right )^{2}} - \frac{11457}{343 \left (3 x + 2\right )^{3}} - \frac{162}{49 \left (3 x + 2\right )^{4}} - \frac{9}{35 \left (3 x + 2\right )^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(1-2*x)/(2+3*x)**6/(3+5*x)**2,x)

[Out]

-128*log(-2*x + 1)/14235529 + 2977686468*log(3*x + 2)/117649 - 3062500*log(5*x +
3)/121 - 15625/(11*(5*x + 3)) - 70752609/(16807*(3*x + 2)) - 806121/(2401*(3*x
+ 2)**2) - 11457/(343*(3*x + 2)**3) - 162/(49*(3*x + 2)**4) - 9/(35*(3*x + 2)**5
)

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Mathematica [A]  time = 0.0637496, size = 95, normalized size = 0.98 \[ -\frac{70752609}{16807 (3 x+2)}-\frac{15625}{55 x+33}-\frac{806121}{2401 (3 x+2)^2}-\frac{11457}{343 (3 x+2)^3}-\frac{162}{49 (3 x+2)^4}-\frac{9}{35 (3 x+2)^5}-\frac{128 \log (1-2 x)}{14235529}+\frac{2977686468 \log (6 x+4)}{117649}-\frac{3062500}{121} \log (10 x+6) \]

Antiderivative was successfully verified.

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

[Out]

-9/(35*(2 + 3*x)^5) - 162/(49*(2 + 3*x)^4) - 11457/(343*(2 + 3*x)^3) - 806121/(2
401*(2 + 3*x)^2) - 70752609/(16807*(2 + 3*x)) - 15625/(33 + 55*x) - (128*Log[1 -
2*x])/14235529 + (2977686468*Log[4 + 6*x])/117649 - (3062500*Log[6 + 10*x])/121

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Maple [A]  time = 0.018, size = 80, normalized size = 0.8 \[ -{\frac{15625}{33+55\,x}}-{\frac{3062500\,\ln \left ( 3+5\,x \right ) }{121}}-{\frac{9}{35\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{162}{49\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{11457}{343\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{806121}{2401\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{70752609}{33614+50421\,x}}+{\frac{2977686468\,\ln \left ( 2+3\,x \right ) }{117649}}-{\frac{128\,\ln \left ( -1+2\,x \right ) }{14235529}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15625/11/(3+5*x)-3062500/121*ln(3+5*x)-9/35/(2+3*x)^5-162/49/(2+3*x)^4-11457/34
3/(2+3*x)^3-806121/2401/(2+3*x)^2-70752609/16807/(2+3*x)[phone]/117649*ln(2+
3*x)-128/14235529*ln(-1+2*x)

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Maxima [A]  time = 1.33121, size = 113, normalized size = 1.16 \[ -\frac{1895084756100 \, x^{5} + 6253779701610 \, x^{4} + 8252743193370 \, x^{3} + 5443759671885 \, x^{2} + 1794885176145 \, x + 236642515057}{924385 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )}} - \frac{3062500}{121} \, \log \left (5 \, x + 3\right ) + \frac{2977686468}{117649} \, \log \left (3 \, x + 2\right ) - \frac{128}{14235529} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/924385*(1895084756100*x^5 + 6253779701610*x^4 + 8252743193370*x^3 + 544375967
1885*x^2 + 1794885176145*x + 236642515057)/(1215*x^6 + 4779*x^5 + 7830*x^4 + 684
0*x^3 + 3360*x^2 + 880*x + 96) - 3062500/121*log(5*x + 3) + 2977686468/117649*lo
g(3*x + 2) - 128/14235529*log(2*x - 1)

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Fricas [A]  time = 0.223359, size = 234, normalized size = 2.41 \[ -\frac{145921526219700 \, x^{5} + 481541037023970 \, x^{4} + 635461225889490 \, x^{3} + 419169494735145 \, x^{2} + 1801500312500 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )} \log \left (5 \, x + 3\right ) - 1801500313140 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )} \log \left (3 \, x + 2\right ) + 640 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )} \log \left (2 \, x - 1\right ) + 138206158563165 \, x + 18221473659389}{71177645 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/71177645*(145921526219700*x^5 + 481541037023970*x^4 + 635461225889490*x^3 + 4
19169494735145*x^2 + 1801500312500*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 +
3360*x^2 + 880*x + 96)*log(5*x + 3) - 1801500313140*(1215*x^6 + 4779*x^5 + 7830*
x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log(3*x + 2) + 640*(1215*x^6 + 4779*x^5
+ 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log(2*x - 1) + 138206158563165*x
+ 18221473659389)/(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x
+ 96)

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Sympy [A]  time = 0.767406, size = 85, normalized size = 0.88 \[ - \frac{1895084756100 x^{5} + 6253779701610 x^{4} + 8252743193370 x^{3} + 5443759671885 x^{2} + 1794885176145 x + 236642515057}{1123127775 x^{6} + 4417635915 x^{5} + 7237934550 x^{4} + 6322793400 x^{3} + 3105933600 x^{2} + 813458800 x + 88740960} - \frac{128 \log{\left (x - \frac{1}{2} \right )}}{14235529} - \frac{3062500 \log{\left (x + \frac{3}{5} \right )}}{121} + \frac{2977686468 \log{\left (x + \frac{2}{3} \right )}}{117649} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(1895084756100*x**5 + 6253779701610*x**4 + 8252743193370*x**3 + 5443759671885*x
**2 + 1794885176145*x + 236642515057)/(1123127775*x**6 + 4417635915*x**5 + 72379
34550*x**4 + 6322793400*x**3 + 3105933600*x**2 + 813458800*x + 88740960) - 128*l
og(x - 1/2)/14235529 - 3062500*log(x + 3/5)/121 + 2977686468*log(x + 2/3)/117649

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GIAC/XCAS [A]  time = 0.212348, size = 123, normalized size = 1.27 \[ -\frac{15625}{11 \,{\left (5 \, x + 3\right )}} + \frac{135 \,{\left (\frac{1627470333}{5 \, x + 3} + \frac{915260769}{{\left (5 \, x + 3\right )}^{2}} + \frac{234430752}{{\left (5 \, x + 3\right )}^{3}} + \frac{23397131}{{\left (5 \, x + 3\right )}^{4}} + 1103836896\right )}}{16807 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{5}} + \frac{2977686468}{117649} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{128}{14235529} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15625/11/(5*x + 3) + 135/16807*(1627470333/(5*x + 3) + 915260769/(5*x + 3)^2 +
234430752/(5*x + 3)^3 + 23397131/(5*x + 3)^4 + 1103836896)/(1/(5*x + 3) + 3)^5 +
2977686468/117649*ln(abs(-1/(5*x + 3) - 3)) - 128/14235529*ln(abs(-11/(5*x + 3)
+ 2))