3.1535 \(\int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^6} \, dx\)

Optimal. Leaf size=87 \[ \frac{176}{117649 (1-2 x)}-\frac{1040}{117649 (3 x+2)}-\frac{194}{16807 (3 x+2)^2}-\frac{128}{7203 (3 x+2)^3}-\frac{31}{1372 (3 x+2)^4}+\frac{1}{245 (3 x+2)^5}-\frac{2608 \log (1-2 x)}{823543}+\frac{2608 \log (3 x+2)}{823543} \]

[Out]

176/(117649*(1 - 2*x)) + 1/(245*(2 + 3*x)^5) - 31/(1372*(2 + 3*x)^4) - 128/(7203
*(2 + 3*x)^3) - 194/(16807*(2 + 3*x)^2) - 1040/(117649*(2 + 3*x)) - (2608*Log[1
- 2*x])/823543 + (2608*Log[2 + 3*x])/823543

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Rubi [A]  time = 0.0956749, antiderivative size = 87, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{176}{117649 (1-2 x)}-\frac{1040}{117649 (3 x+2)}-\frac{194}{16807 (3 x+2)^2}-\frac{128}{7203 (3 x+2)^3}-\frac{31}{1372 (3 x+2)^4}+\frac{1}{245 (3 x+2)^5}-\frac{2608 \log (1-2 x)}{823543}+\frac{2608 \log (3 x+2)}{823543} \]

Antiderivative was successfully verified.

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

[Out]

176/(117649*(1 - 2*x)) + 1/(245*(2 + 3*x)^5) - 31/(1372*(2 + 3*x)^4) - 128/(7203
*(2 + 3*x)^3) - 194/(16807*(2 + 3*x)^2) - 1040/(117649*(2 + 3*x)) - (2608*Log[1
- 2*x])/823543 + (2608*Log[2 + 3*x])/823543

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Rubi in Sympy [A]  time = 12.422, size = 73, normalized size = 0.84 \[ - \frac{2608 \log{\left (- 2 x + 1 \right )}}{823543} + \frac{2608 \log{\left (3 x + 2 \right )}}{823543} - \frac{1040}{117649 \left (3 x + 2\right )} - \frac{194}{16807 \left (3 x + 2\right )^{2}} - \frac{128}{7203 \left (3 x + 2\right )^{3}} - \frac{31}{1372 \left (3 x + 2\right )^{4}} + \frac{1}{245 \left (3 x + 2\right )^{5}} + \frac{176}{117649 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2608*log(-2*x + 1)/823543 + 2608*log(3*x + 2)/823543 - 1040/(117649*(3*x + 2))
- 194/(16807*(3*x + 2)**2) - 128/(7203*(3*x + 2)**3) - 31/(1372*(3*x + 2)**4) +
1/(245*(3*x + 2)**5) + 176/(117649*(-2*x + 1))

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Mathematica [A]  time = 0.0811167, size = 62, normalized size = 0.71 \[ \frac{-\frac{7 \left (12674880 x^5+34855920 x^4+33741000 x^3+10410810 x^2-3488689 x-2104258\right )}{(2 x-1) (3 x+2)^5}-156480 \log (3-6 x)+156480 \log (3 x+2)}{49412580} \]

Antiderivative was successfully verified.

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

[Out]

((-7*(-2104258 - 3488689*x + 10410810*x^2 + 33741000*x^3 + 34855920*x^4 + 126748
80*x^5))/((-1 + 2*x)*(2 + 3*x)^5) - 156480*Log[3 - 6*x] + 156480*Log[2 + 3*x])/4
9412580

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Maple [A]  time = 0.014, size = 72, normalized size = 0.8 \[{\frac{1}{245\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{31}{1372\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{128}{7203\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{194}{16807\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{1040}{235298+352947\,x}}+{\frac{2608\,\ln \left ( 2+3\,x \right ) }{823543}}-{\frac{176}{-117649+235298\,x}}-{\frac{2608\,\ln \left ( -1+2\,x \right ) }{823543}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/245/(2+3*x)^5-31/1372/(2+3*x)^4-128/7203/(2+3*x)^3-194/16807/(2+3*x)^2-1040/11
7649/(2+3*x)+2608/823543*ln(2+3*x)-176/117649/(-1+2*x)-2608/823543*ln(-1+2*x)

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Maxima [A]  time = 1.33509, size = 103, normalized size = 1.18 \[ -\frac{12674880 \, x^{5} + 34855920 \, x^{4} + 33741000 \, x^{3} + 10410810 \, x^{2} - 3488689 \, x - 2104258}{7058940 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} + \frac{2608}{823543} \, \log \left (3 \, x + 2\right ) - \frac{2608}{823543} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/7058940*(12674880*x^5 + 34855920*x^4 + 33741000*x^3 + 10410810*x^2 - 3488689*
x - 2104258)/(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32) +
2608/823543*log(3*x + 2) - 2608/823543*log(2*x - 1)

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Fricas [A]  time = 0.220427, size = 182, normalized size = 2.09 \[ -\frac{88724160 \, x^{5} + 243991440 \, x^{4} + 236187000 \, x^{3} + 72875670 \, x^{2} - 156480 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (3 \, x + 2\right ) + 156480 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (2 \, x - 1\right ) - 24420823 \, x - 14729806}{49412580 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/49412580*(88724160*x^5 + 243991440*x^4 + 236187000*x^3 + 72875670*x^2 - 15648
0*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(3*x + 2)
+ 156480*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(2*
x - 1) - 24420823*x - 14729806)/(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x
^2 - 176*x - 32)

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Sympy [A]  time = 0.523759, size = 75, normalized size = 0.86 \[ - \frac{12674880 x^{5} + 34855920 x^{4} + 33741000 x^{3} + 10410810 x^{2} - 3488689 x - 2104258}{3430644840 x^{6} + 9720160380 x^{5} + 9529569000 x^{4} + 2541218400 x^{3} - 1694145600 x^{2} - 1242373440 x - 225886080} - \frac{2608 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{2608 \log{\left (x + \frac{2}{3} \right )}}{823543} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(12674880*x**5 + 34855920*x**4 + 33741000*x**3 + 10410810*x**2 - 3488689*x - 21
04258)/(3430644840*x**6 + 9720160380*x**5 + 9529569000*x**4 + 2541218400*x**3 -
1694145600*x**2 - 1242373440*x - 225886080) - 2608*log(x - 1/2)/823543 + 2608*lo
g(x + 2/3)/823543

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GIAC/XCAS [A]  time = 0.207714, size = 105, normalized size = 1.21 \[ -\frac{176}{117649 \,{\left (2 \, x - 1\right )}} + \frac{12 \,{\left (\frac{3424365}{2 \, x - 1} + \frac{13259400}{{\left (2 \, x - 1\right )}^{2}} + \frac{23152500}{{\left (2 \, x - 1\right )}^{3}} + \frac{15366400}{{\left (2 \, x - 1\right )}^{4}} + 335637\right )}}{4117715 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{5}} + \frac{2608}{823543} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-176/117649/(2*x - 1) + 12/4117715*(3424365/(2*x - 1) + 13259400/(2*x - 1)^2 + 2
3152500/(2*x - 1)^3 + 15366400/(2*x - 1)^4 + 335637)/(7/(2*x - 1) + 3)^5 + 2608/
823543*ln(abs(-7/(2*x - 1) - 3))