3.1302 \(\int \frac{(1-2 x)^2}{(2+3 x)^7 (3+5 x)^2} \, dx\)

Optimal. Leaf size=90 \[ -\frac{277750}{3 x+2}-\frac{75625}{5 x+3}-\frac{46475}{2 (3 x+2)^2}-\frac{7480}{3 (3 x+2)^3}-\frac{1133}{4 (3 x+2)^4}-\frac{154}{5 (3 x+2)^5}-\frac{49}{18 (3 x+2)^6}+1615625 \log (3 x+2)-1615625 \log (5 x+3) \]

[Out]

-49/(18*(2 + 3*x)^6) - 154/(5*(2 + 3*x)^5) - 1133/(4*(2 + 3*x)^4) - 7480/(3*(2 +
3*x)^3) - 46475/(2*(2 + 3*x)^2) - 277750/(2 + 3*x) - 75625/(3 + 5*x) + 1615625*
Log[2 + 3*x] - 1615625*Log[3 + 5*x]

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Rubi [A]  time = 0.10182, antiderivative size = 90, 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 \[ -\frac{277750}{3 x+2}-\frac{75625}{5 x+3}-\frac{46475}{2 (3 x+2)^2}-\frac{7480}{3 (3 x+2)^3}-\frac{1133}{4 (3 x+2)^4}-\frac{154}{5 (3 x+2)^5}-\frac{49}{18 (3 x+2)^6}+1615625 \log (3 x+2)-1615625 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-49/(18*(2 + 3*x)^6) - 154/(5*(2 + 3*x)^5) - 1133/(4*(2 + 3*x)^4) - 7480/(3*(2 +
3*x)^3) - 46475/(2*(2 + 3*x)^2) - 277750/(2 + 3*x) - 75625/(3 + 5*x) + 1615625*
Log[2 + 3*x] - 1615625*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 13.3493, size = 80, normalized size = 0.89 \[ 1615625 \log{\left (3 x + 2 \right )} - 1615625 \log{\left (5 x + 3 \right )} - \frac{75625}{5 x + 3} - \frac{277750}{3 x + 2} - \frac{46475}{2 \left (3 x + 2\right )^{2}} - \frac{7480}{3 \left (3 x + 2\right )^{3}} - \frac{1133}{4 \left (3 x + 2\right )^{4}} - \frac{154}{5 \left (3 x + 2\right )^{5}} - \frac{49}{18 \left (3 x + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2/(2+3*x)**7/(3+5*x)**2,x)

[Out]

1615625*log(3*x + 2) - 1615625*log(5*x + 3) - 75625/(5*x + 3) - 277750/(3*x + 2)
- 46475/(2*(3*x + 2)**2) - 7480/(3*(3*x + 2)**3) - 1133/(4*(3*x + 2)**4) - 154/
(5*(3*x + 2)**5) - 49/(18*(3*x + 2)**6)

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Mathematica [A]  time = 0.158242, size = 92, normalized size = 1.02 \[ -\frac{277750}{3 x+2}-\frac{75625}{5 x+3}-\frac{46475}{2 (3 x+2)^2}-\frac{7480}{3 (3 x+2)^3}-\frac{1133}{4 (3 x+2)^4}-\frac{154}{5 (3 x+2)^5}-\frac{49}{18 (3 x+2)^6}+1615625 \log (5 (3 x+2))-1615625 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-49/(18*(2 + 3*x)^6) - 154/(5*(2 + 3*x)^5) - 1133/(4*(2 + 3*x)^4) - 7480/(3*(2 +
3*x)^3) - 46475/(2*(2 + 3*x)^2) - 277750/(2 + 3*x) - 75625/(3 + 5*x) + 1615625*
Log[5*(2 + 3*x)] - 1615625*Log[3 + 5*x]

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Maple [A]  time = 0.017, size = 81, normalized size = 0.9 \[ -{\frac{49}{18\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{154}{5\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{1133}{4\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{7480}{3\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{46475}{2\, \left ( 2+3\,x \right ) ^{2}}}-277750\, \left ( 2+3\,x \right ) ^{-1}-75625\, \left ( 3+5\,x \right ) ^{-1}+1615625\,\ln \left ( 2+3\,x \right ) -1615625\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-49/18/(2+3*x)^6-154/5/(2+3*x)^5-1133/4/(2+3*x)^4-7480/3/(2+3*x)^3-46475/2/(2+3*
x)^2-277750/(2+3*x)-75625/(3+5*x)+1615625*ln(2+3*x)-1615625*ln(3+5*x)

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Maxima [A]  time = 1.32981, size = 116, normalized size = 1.29 \[ -\frac{70667437500 \, x^{6} + 280314168750 \, x^{5} + 463211966250 \, x^{4} + 408159415125 \, x^{3} + 202262350455 \, x^{2} + 53445037346 \, x + 5882909754}{180 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )}} - 1615625 \, \log \left (5 \, x + 3\right ) + 1615625 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/180*(70667437500*x^6 + 280314168750*x^5 + 463211966250*x^4 + 408159415125*x^3
+ 202262350455*x^2 + 53445037346*x + 5882909754)/(3645*x^7 + 16767*x^6 + 33048*
x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192) - 1615625*log(5*x + 3) +
1615625*log(3*x + 2)

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Fricas [A]  time = 0.217344, size = 209, normalized size = 2.32 \[ -\frac{70667437500 \, x^{6} + 280314168750 \, x^{5} + 463211966250 \, x^{4} + 408159415125 \, x^{3} + 202262350455 \, x^{2} + 290812500 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )} \log \left (5 \, x + 3\right ) - 290812500 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )} \log \left (3 \, x + 2\right ) + 53445037346 \, x + 5882909754}{180 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/180*(70667437500*x^6 + 280314168750*x^5 + 463211966250*x^4 + 408159415125*x^3
+ 202262350455*x^2 + 290812500*(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*x^4 +
23760*x^3 + 9360*x^2 + 2048*x + 192)*log(5*x + 3) - 290812500*(3645*x^7 + 16767*
x^6 + 33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)*log(3*x + 2)
+ 53445037346*x + 5882909754)/(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*x^4 + 23
760*x^3 + 9360*x^2 + 2048*x + 192)

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Sympy [A]  time = 0.607487, size = 82, normalized size = 0.91 \[ - \frac{70667437500 x^{6} + 280314168750 x^{5} + 463211966250 x^{4} + 408159415125 x^{3} + 202262350455 x^{2} + 53445037346 x + 5882909754}{656100 x^{7} + 3018060 x^{6} + 5948640 x^{5} + 6512400 x^{4} + 4276800 x^{3} + 1684800 x^{2} + 368640 x + 34560} - 1615625 \log{\left (x + \frac{3}{5} \right )} + 1615625 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(70667437500*x**6 + 280314168750*x**5 + 463211966250*x**4 + 408159415125*x**3 +
202262350455*x**2 + 53445037346*x + 5882909754)/(656100*x**7 + 3018060*x**6 + 5
948640*x**5 + 6512400*x**4 + 4276800*x**3 + 1684800*x**2 + 368640*x + 34560) - 1
615625*log(x + 3/5) + 1615625*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.213298, size = 115, normalized size = 1.28 \[ -\frac{75625}{5 \, x + 3} + \frac{625 \,{\left (\frac{22074930}{5 \, x + 3} + \frac{16294797}{{\left (5 \, x + 3\right )}^{2}} + \frac{6120660}{{\left (5 \, x + 3\right )}^{3}} + \frac{1179210}{{\left (5 \, x + 3\right )}^{4}} + \frac{94660}{{\left (5 \, x + 3\right )}^{5}} + 12117357\right )}}{4 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{6}} + 1615625 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-75625/(5*x + 3) + 625/4*(22074930/(5*x + 3) + 16294797/(5*x + 3)^2 + 6120660/(5
*x + 3)^3 + 1179210/(5*x + 3)^4 + 94660/(5*x + 3)^5 + 12117357)/(1/(5*x + 3) + 3
)^6 + 1615625*ln(abs(-1/(5*x + 3) - 3))