3.1318 \(\int \frac{(1-2 x)^2}{(2+3 x)^6 (3+5 x)^3} \, dx\)

Optimal. Leaf size=88 \[ \frac{424975}{3 x+2}+\frac{277750}{5 x+3}+\frac{28555}{(3 x+2)^2}-\frac{15125}{2 (5 x+3)^2}+\frac{6934}{3 (3 x+2)^3}+\frac{707}{4 (3 x+2)^4}+\frac{49}{5 (3 x+2)^5}-2958125 \log (3 x+2)+2958125 \log (5 x+3) \]

[Out]

49/(5*(2 + 3*x)^5) + 707/(4*(2 + 3*x)^4) + 6934/(3*(2 + 3*x)^3) + 28555/(2 + 3*x
)^2 + 424975/(2 + 3*x) - 15125/(2*(3 + 5*x)^2) + 277750/(3 + 5*x) - 2958125*Log[
2 + 3*x] + 2958125*Log[3 + 5*x]

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Rubi [A]  time = 0.11011, antiderivative size = 88, 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 \[ \frac{424975}{3 x+2}+\frac{277750}{5 x+3}+\frac{28555}{(3 x+2)^2}-\frac{15125}{2 (5 x+3)^2}+\frac{6934}{3 (3 x+2)^3}+\frac{707}{4 (3 x+2)^4}+\frac{49}{5 (3 x+2)^5}-2958125 \log (3 x+2)+2958125 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

49/(5*(2 + 3*x)^5) + 707/(4*(2 + 3*x)^4) + 6934/(3*(2 + 3*x)^3) + 28555/(2 + 3*x
)^2 + 424975/(2 + 3*x) - 15125/(2*(3 + 5*x)^2) + 277750/(3 + 5*x) - 2958125*Log[
2 + 3*x] + 2958125*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 13.8014, size = 78, normalized size = 0.89 \[ - 2958125 \log{\left (3 x + 2 \right )} + 2958125 \log{\left (5 x + 3 \right )} + \frac{277750}{5 x + 3} - \frac{15125}{2 \left (5 x + 3\right )^{2}} + \frac{424975}{3 x + 2} + \frac{28555}{\left (3 x + 2\right )^{2}} + \frac{6934}{3 \left (3 x + 2\right )^{3}} + \frac{707}{4 \left (3 x + 2\right )^{4}} + \frac{49}{5 \left (3 x + 2\right )^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2958125*log(3*x + 2) + 2958125*log(5*x + 3) + 277750/(5*x + 3) - 15125/(2*(5*x
+ 3)**2) + 424975/(3*x + 2) + 28555/(3*x + 2)**2 + 6934/(3*(3*x + 2)**3) + 707/(
4*(3*x + 2)**4) + 49/(5*(3*x + 2)**5)

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Mathematica [A]  time = 0.106172, size = 90, normalized size = 1.02 \[ \frac{424975}{3 x+2}+\frac{277750}{5 x+3}+\frac{28555}{(3 x+2)^2}-\frac{15125}{2 (5 x+3)^2}+\frac{6934}{3 (3 x+2)^3}+\frac{707}{4 (3 x+2)^4}+\frac{49}{5 (3 x+2)^5}-2958125 \log (5 (3 x+2))+2958125 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

49/(5*(2 + 3*x)^5) + 707/(4*(2 + 3*x)^4) + 6934/(3*(2 + 3*x)^3) + 28555/(2 + 3*x
)^2 + 424975/(2 + 3*x) - 15125/(2*(3 + 5*x)^2) + 277750/(3 + 5*x) - 2958125*Log[
5*(2 + 3*x)] + 2958125*Log[3 + 5*x]

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Maple [A]  time = 0.016, size = 81, normalized size = 0.9 \[{\frac{49}{5\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{707}{4\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{6934}{3\, \left ( 2+3\,x \right ) ^{3}}}+28555\, \left ( 2+3\,x \right ) ^{-2}+424975\, \left ( 2+3\,x \right ) ^{-1}-{\frac{15125}{2\, \left ( 3+5\,x \right ) ^{2}}}+277750\, \left ( 3+5\,x \right ) ^{-1}-2958125\,\ln \left ( 2+3\,x \right ) +2958125\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

49/5/(2+3*x)^5+707/4/(2+3*x)^4+6934/3/(2+3*x)^3+28555/(2+3*x)^2+424975/(2+3*x)-1
5125/2/(3+5*x)^2+277750/(3+5*x)-2958125*ln(2+3*x)+2958125*ln(3+5*x)

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Maxima [A]  time = 1.47891, size = 116, normalized size = 1.32 \[ \frac{71882437500 \, x^{6} + 280341506250 \, x^{5} + 455361930000 \, x^{4} + 394308004875 \, x^{3} + 191974077080 \, x^{2} + 49825144515 \, x + 5385650262}{60 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )}} + 2958125 \, \log \left (5 \, x + 3\right ) - 2958125 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/60*(71882437500*x^6 + 280341506250*x^5 + 455361930000*x^4 + 394308004875*x^3 +
191974077080*x^2 + 49825144515*x + 5385650262)/(6075*x^7 + 27540*x^6 + 53487*x^
5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288) + 2958125*log(5*x + 3) - 2
958125*log(3*x + 2)

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Fricas [A]  time = 0.20974, size = 209, normalized size = 2.38 \[ \frac{71882437500 \, x^{6} + 280341506250 \, x^{5} + 455361930000 \, x^{4} + 394308004875 \, x^{3} + 191974077080 \, x^{2} + 177487500 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )} \log \left (5 \, x + 3\right ) - 177487500 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )} \log \left (3 \, x + 2\right ) + 49825144515 \, x + 5385650262}{60 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/60*(71882437500*x^6 + 280341506250*x^5 + 455361930000*x^4 + 394308004875*x^3 +
191974077080*x^2 + 177487500*(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37
320*x^3 + 14480*x^2 + 3120*x + 288)*log(5*x + 3) - 177487500*(6075*x^7 + 27540*x
^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288)*log(3*x + 2)
+ 49825144515*x + 5385650262)/(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37
320*x^3 + 14480*x^2 + 3120*x + 288)

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Sympy [A]  time = 0.594023, size = 82, normalized size = 0.93 \[ \frac{71882437500 x^{6} + 280341506250 x^{5} + 455361930000 x^{4} + 394308004875 x^{3} + 191974077080 x^{2} + 49825144515 x + 5385650262}{364500 x^{7} + 1652400 x^{6} + 3209220 x^{5} + 3461400 x^{4} + 2239200 x^{3} + 868800 x^{2} + 187200 x + 17280} + 2958125 \log{\left (x + \frac{3}{5} \right )} - 2958125 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(71882437500*x**6 + 280341506250*x**5 + 455361930000*x**4 + 394308004875*x**3 +
191974077080*x**2 + 49825144515*x + 5385650262)/(364500*x**7 + 1652400*x**6 + 32
09220*x**5 + 3461400*x**4 + 2239200*x**3 + 868800*x**2 + 187200*x + 17280) + 295
8125*log(x + 3/5) - 2958125*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.208012, size = 88, normalized size = 1. \[ \frac{71882437500 \, x^{6} + 280341506250 \, x^{5} + 455361930000 \, x^{4} + 394308004875 \, x^{3} + 191974077080 \, x^{2} + 49825144515 \, x + 5385650262}{60 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{5}} + 2958125 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 2958125 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/60*(71882437500*x^6 + 280341506250*x^5 + 455361930000*x^4 + 394308004875*x^3 +
191974077080*x^2 + 49825144515*x + 5385650262)/((5*x + 3)^2*(3*x + 2)^5) + 2958
125*ln(abs(5*x + 3)) - 2958125*ln(abs(3*x + 2))