3.1415 \(\int \frac{(1-2 x)^3}{(2+3 x)^7 (3+5 x)^3} \, dx\)

Optimal. Leaf size=97 \[ \frac{6618975}{3 x+2}+\frac{3584625}{5 x+3}+\frac{953535}{2 (3 x+2)^2}-\frac{166375}{2 (5 x+3)^2}+\frac{42878}{(3 x+2)^3}+\frac{3927}{(3 x+2)^4}+\frac{1617}{5 (3 x+2)^5}+\frac{343}{18 (3 x+2)^6}-43848750 \log (3 x+2)[phone] \log (5 x+3) \]

[Out]

343/(18*(2 + 3*x)^6) + 1617/(5*(2 + 3*x)^5) + 3927/(2 + 3*x)^4 + 42878/(2 + 3*x)
^3 + 953535/(2*(2 + 3*x)^2) + 6618975/(2 + 3*x) - 166375/(2*(3 + 5*x)^2) + 35846
25/(3 + 5*x) - 43848750*Log[2 + 3*x] + 43848750*Log[3 + 5*x]

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Rubi [A]  time = 0.123985, 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 \[ \frac{6618975}{3 x+2}+\frac{3584625}{5 x+3}+\frac{953535}{2 (3 x+2)^2}-\frac{166375}{2 (5 x+3)^2}+\frac{42878}{(3 x+2)^3}+\frac{3927}{(3 x+2)^4}+\frac{1617}{5 (3 x+2)^5}+\frac{343}{18 (3 x+2)^6}-43848750 \log (3 x+2)[phone] \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

343/(18*(2 + 3*x)^6) + 1617/(5*(2 + 3*x)^5) + 3927/(2 + 3*x)^4 + 42878/(2 + 3*x)
^3 + 953535/(2*(2 + 3*x)^2) + 6618975/(2 + 3*x) - 166375/(2*(3 + 5*x)^2) + 35846
25/(3 + 5*x) - 43848750*Log[2 + 3*x] + 43848750*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 15.4558, size = 87, normalized size = 0.9 \[ - 43848750 \log{\left (3 x + 2 \right )} + 43848750 \log{\left (5 x + 3 \right )} + \frac{3584625}{5 x + 3} - \frac{166375}{2 \left (5 x + 3\right )^{2}} + \frac{6618975}{3 x + 2} + \frac{953535}{2 \left (3 x + 2\right )^{2}} + \frac{42878}{\left (3 x + 2\right )^{3}} + \frac{3927}{\left (3 x + 2\right )^{4}} + \frac{1617}{5 \left (3 x + 2\right )^{5}} + \frac{343}{18 \left (3 x + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-43848750*log(3*x + 2) + 43848750*log(5*x + 3) + 3584625/(5*x + 3) - 166375/(2*(
5*x + 3)**2) + 6618975/(3*x + 2) + 953535/(2*(3*x + 2)**2) + 42878/(3*x + 2)**3
+ 3927/(3*x + 2)**4 + 1617/(5*(3*x + 2)**5) + 343/(18*(3*x + 2)**6)

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Mathematica [A]  time = 0.172259, size = 99, normalized size = 1.02 \[ \frac{6618975}{3 x+2}+\frac{3584625}{5 x+3}+\frac{953535}{2 (3 x+2)^2}-\frac{166375}{2 (5 x+3)^2}+\frac{42878}{(3 x+2)^3}+\frac{3927}{(3 x+2)^4}+\frac{1617}{5 (3 x+2)^5}+\frac{343}{18 (3 x+2)^6}-43848750 \log (5 (3 x+2))[phone] \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

343/(18*(2 + 3*x)^6) + 1617/(5*(2 + 3*x)^5) + 3927/(2 + 3*x)^4 + 42878/(2 + 3*x)
^3 + 953535/(2*(2 + 3*x)^2) + 6618975/(2 + 3*x) - 166375/(2*(3 + 5*x)^2) + 35846
25/(3 + 5*x) - 43848750*Log[5*(2 + 3*x)] + 43848750*Log[3 + 5*x]

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Maple [A]  time = 0.016, size = 90, normalized size = 0.9 \[{\frac{343}{18\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{1617}{5\, \left ( 2+3\,x \right ) ^{5}}}+3927\, \left ( 2+3\,x \right ) ^{-4}+42878\, \left ( 2+3\,x \right ) ^{-3}+{\frac{953535}{2\, \left ( 2+3\,x \right ) ^{2}}}+6618975\, \left ( 2+3\,x \right ) ^{-1}-{\frac{166375}{2\, \left ( 3+5\,x \right ) ^{2}}}+3584625\, \left ( 3+5\,x \right ) ^{-1}-43848750\,\ln \left ( 2+3\,x \right ) [phone]\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343/18/(2+3*x)^6+1617/5/(2+3*x)^5+3927/(2+3*x)^4+42878/(2+3*x)^3+953535/2/(2+3*x
)^2+6618975/(2+3*x)-166375/2/(3+5*x)^2+3584625/(3+5*x)-43848750*ln(2+3*x)+438487
50*ln(3+5*x)

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Maxima [A]  time = 1.3591, size = 130, normalized size = 1.34 \[ \frac{4794860812500 \, x^{7} + 21896531043750 \, x^{6} + 42841193422500 \, x^{5} + 46551705341625 \, x^{4} + 30340145968110 \, x^{3} + 11860532030465 \, x^{2} + 2574943269792 \, x + 239497011063}{90 \,{\left (18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right )}} + 43848750 \, \log \left (5 \, x + 3\right ) - 43848750 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/90*(4794860812500*x^7 + 21896531043750*x^6 + 42841193422500*x^5 + 465517053416
25*x^4 + 30340145968110*x^3 + 11860532030465*x^2 + 2574943269792*x + 23949701106
3)/(18225*x^8 + 94770*x^7 + 215541*x^6 + 280044*x^5 + 227340*x^4 + 118080*x^3 +
38320*x^2 + 7104*x + 576) + 43848750*log(5*x + 3) - 43848750*log(3*x + 2)

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Fricas [A]  time = 0.212674, size = 236, normalized size = 2.43 \[ \frac{4794860812500 \, x^{7} + 21896531043750 \, x^{6} + 42841193422500 \, x^{5} + 46551705341625 \, x^{4} + 30340145968110 \, x^{3} + 11860532030465 \, x^{2} + 3946387500 \,{\left (18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right )} \log \left (5 \, x + 3\right ) - 3946387500 \,{\left (18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right )} \log \left (3 \, x + 2\right ) + 2574943269792 \, x + 239497011063}{90 \,{\left (18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/90*(4794860812500*x^7 + 21896531043750*x^6 + 42841193422500*x^5 + 465517053416
25*x^4 + 30340145968110*x^3 + 11860532030465*x^2 + 3946387500*(18225*x^8 + 94770
*x^7 + 215541*x^6 + 280044*x^5 + 227340*x^4 + 118080*x^3 + 38320*x^2 + 7104*x +
576)*log(5*x + 3) - 3946387500*(18225*x^8 + 94770*x^7 + 215541*x^6 + 280044*x^5
+ 227340*x^4 + 118080*x^3 + 38320*x^2 + 7104*x + 576)*log(3*x + 2) + 25749432697
92*x + 239497011063)/(18225*x^8 + 94770*x^7 + 215541*x^6 + 280044*x^5 + 227340*x
^4 + 118080*x^3 + 38320*x^2 + 7104*x + 576)

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Sympy [A]  time = 0.681235, size = 92, normalized size = 0.95 \[ \frac{4794860812500 x^{7} + 21896531043750 x^{6} + 42841193422500 x^{5} + 46551705341625 x^{4} + 30340145968110 x^{3} + 11860532030465 x^{2} + 2574943269792 x + 239497011063}{1640250 x^{8} + 8529300 x^{7} + 19398690 x^{6} + 25203960 x^{5} + 20460600 x^{4} + 10627200 x^{3} + 3448800 x^{2} + 639360 x + 51840} + 43848750 \log{\left (x + \frac{3}{5} \right )} - 43848750 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(4794860812500*x**7 + 21896531043750*x**6 + 42841193422500*x**5 + 46551705341625
*x**4 + 30340145968110*x**3 + 11860532030465*x**2 + 2574943269792*x + 2394970110
63)/(1640250*x**8 + 8529300*x**7 + 19398690*x**6 + 25203960*x**5 + 20460600*x**4
+ 10627200*x**3 + 3448800*x**2 + 639360*x + 51840) + 43848750*log(x + 3/5) - 43
848750*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.213181, size = 95, normalized size = 0.98 \[ \frac{4794860812500 \, x^{7} + 21896531043750 \, x^{6} + 42841193422500 \, x^{5} + 46551705341625 \, x^{4} + 30340145968110 \, x^{3} + 11860532030465 \, x^{2} + 2574943269792 \, x + 239497011063}{90 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{6}} + 43848750 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 43848750 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/90*(4794860812500*x^7 + 21896531043750*x^6 + 42841193422500*x^5 + 465517053416
25*x^4 + 30340145968110*x^3 + 11860532030465*x^2 + 2574943269792*x + 23949701106
3)/((5*x + 3)^2*(3*x + 2)^6) + 43848750*ln(abs(5*x + 3)) - 43848750*ln(abs(3*x +
2))