3.1319 \(\int \frac{(1-2 x)^2}{(2+3 x)^7 (3+5 x)^3} \, dx\)

Optimal. Leaf size=101 \[ \frac{2958125}{3 x+2}+\frac{1615625}{5 x+3}+\frac{424975}{2 (3 x+2)^2}-\frac{75625}{2 (5 x+3)^2}+\frac{57110}{3 (3 x+2)^3}+\frac{3467}{2 (3 x+2)^4}+\frac{707}{5 (3 x+2)^5}+\frac{49}{6 (3 x+2)^6}-19637500 \log (3 x+2)[phone] \log (5 x+3) \]

[Out]

49/(6*(2 + 3*x)^6) + 707/(5*(2 + 3*x)^5) + 3467/(2*(2 + 3*x)^4) + 57110/(3*(2 +
3*x)^3) + 424975/(2*(2 + 3*x)^2) + 2958125/(2 + 3*x) - 75625/(2*(3 + 5*x)^2) + 1
615625/(3 + 5*x) - 19637500*Log[2 + 3*x] + 19637500*Log[3 + 5*x]

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Rubi [A]  time = 0.123635, antiderivative size = 101, 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 \[ \frac{2958125}{3 x+2}+\frac{1615625}{5 x+3}+\frac{424975}{2 (3 x+2)^2}-\frac{75625}{2 (5 x+3)^2}+\frac{57110}{3 (3 x+2)^3}+\frac{3467}{2 (3 x+2)^4}+\frac{707}{5 (3 x+2)^5}+\frac{49}{6 (3 x+2)^6}-19637500 \log (3 x+2)[phone] \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

49/(6*(2 + 3*x)^6) + 707/(5*(2 + 3*x)^5) + 3467/(2*(2 + 3*x)^4) + 57110/(3*(2 +
3*x)^3) + 424975/(2*(2 + 3*x)^2) + 2958125/(2 + 3*x) - 75625/(2*(3 + 5*x)^2) + 1
615625/(3 + 5*x) - 19637500*Log[2 + 3*x] + 19637500*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 15.2602, size = 90, normalized size = 0.89 \[ - 19637500 \log{\left (3 x + 2 \right )} + 19637500 \log{\left (5 x + 3 \right )} + \frac{1615625}{5 x + 3} - \frac{75625}{2 \left (5 x + 3\right )^{2}} + \frac{2958125}{3 x + 2} + \frac{424975}{2 \left (3 x + 2\right )^{2}} + \frac{57110}{3 \left (3 x + 2\right )^{3}} + \frac{3467}{2 \left (3 x + 2\right )^{4}} + \frac{707}{5 \left (3 x + 2\right )^{5}} + \frac{49}{6 \left (3 x + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-19637500*log(3*x + 2) + 19637500*log(5*x + 3) + 1615625/(5*x + 3) - 75625/(2*(5
*x + 3)**2) + 2958125/(3*x + 2) + 424975/(2*(3*x + 2)**2) + 57110/(3*(3*x + 2)**
3) + 3467/(2*(3*x + 2)**4) + 707/(5*(3*x + 2)**5) + 49/(6*(3*x + 2)**6)

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Mathematica [A]  time = 0.119727, size = 103, normalized size = 1.02 \[ \frac{2958125}{3 x+2}+\frac{1615625}{5 x+3}+\frac{424975}{2 (3 x+2)^2}-\frac{75625}{2 (5 x+3)^2}+\frac{57110}{3 (3 x+2)^3}+\frac{3467}{2 (3 x+2)^4}+\frac{707}{5 (3 x+2)^5}+\frac{49}{6 (3 x+2)^6}-19637500 \log (5 (3 x+2))[phone] \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

49/(6*(2 + 3*x)^6) + 707/(5*(2 + 3*x)^5) + 3467/(2*(2 + 3*x)^4) + 57110/(3*(2 +
3*x)^3) + 424975/(2*(2 + 3*x)^2) + 2958125/(2 + 3*x) - 75625/(2*(3 + 5*x)^2) + 1
615625/(3 + 5*x) - 19637500*Log[5*(2 + 3*x)] + 19637500*Log[3 + 5*x]

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Maple [A]  time = 0.016, size = 90, normalized size = 0.9 \[{\frac{49}{6\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{707}{5\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{3467}{2\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{57110}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{424975}{2\, \left ( 2+3\,x \right ) ^{2}}}+2958125\, \left ( 2+3\,x \right ) ^{-1}-{\frac{75625}{2\, \left ( 3+5\,x \right ) ^{2}}}+1615625\, \left ( 3+5\,x \right ) ^{-1}-19637500\,\ln \left ( 2+3\,x \right ) [phone]\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

49/6/(2+3*x)^6+707/5/(2+3*x)^5+3467/2/(2+3*x)^4+57110/3/(2+3*x)^3+424975/2/(2+3*
x)^2+2958125/(2+3*x)-75625/2/(3+5*x)^2+1615625/(3+5*x)-19637500*ln(2+3*x)+196375
00*ln(3+5*x)

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Maxima [A]  time = 1.35253, size = 130, normalized size = 1.29 \[ \frac{238595625000 \, x^{7} + 1089586687500 \, x^{6} + 2131807725000 \, x^{5} + 2316445391250 \, x^{4} + 1509746867100 \, x^{3} + 590188362770 \, x^{2} + 128130976648 \, x + 11917538647}{10 \,{\left (18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right )}} + 19637500 \, \log \left (5 \, x + 3\right ) - 19637500 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/10*(238595625000*x^7 + 1089586687500*x^6 + 2131807725000*x^5 + 2316445391250*x
^4 + 1509746867100*x^3 + 590188362770*x^2 + 128130976648*x + 11917538647)/(18225
*x^8 + 94770*x^7 + 215541*x^6 + 280044*x^5 + 227340*x^4 + 118080*x^3 + 38320*x^2
+ 7104*x + 576) + 19637500*log(5*x + 3) - 19637500*log(3*x + 2)

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Fricas [A]  time = 0.212672, size = 236, normalized size = 2.34 \[ \frac{238595625000 \, x^{7} + 1089586687500 \, x^{6} + 2131807725000 \, x^{5} + 2316445391250 \, x^{4} + 1509746867100 \, x^{3} + 590188362770 \, x^{2} + 196375000 \,{\left (18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right )} \log \left (5 \, x + 3\right ) - 196375000 \,{\left (18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right )} \log \left (3 \, x + 2\right ) + 128130976648 \, x + 11917538647}{10 \,{\left (18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/10*(238595625000*x^7 + 1089586687500*x^6 + 2131807725000*x^5 + 2316445391250*x
^4 + 1509746867100*x^3 + 590188362770*x^2 + 196375000*(18225*x^8 + 94770*x^7 + 2
15541*x^6 + 280044*x^5 + 227340*x^4 + 118080*x^3 + 38320*x^2 + 7104*x + 576)*log
(5*x + 3) - 196375000*(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) + 128130976648*x + 119
17538647)/(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 = 0.666344, size = 92, normalized size = 0.91 \[ \frac{238595625000 x^{7} + 1089586687500 x^{6} + 2131807725000 x^{5} + 2316445391250 x^{4} + 1509746867100 x^{3} + 590188362770 x^{2} + 128130976648 x + 11917538647}{182250 x^{8} + 947700 x^{7} + 2155410 x^{6} + 2800440 x^{5} + 2273400 x^{4} + 1180800 x^{3} + 383200 x^{2} + 71040 x + 5760} + 19637500 \log{\left (x + \frac{3}{5} \right )} - 19637500 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(238595625000*x**7 + 1089586687500*x**6 + 2131807725000*x**5 + 2316445391250*x**
4 + 1509746867100*x**3 + 590188362770*x**2 + 128130976648*x + 11917538647)/(1822
50*x**8 + 947700*x**7 + 2155410*x**6 + 2800440*x**5 + 2273400*x**4 + 1180800*x**
3 + 383200*x**2 + 71040*x + 5760) + 19637500*log(x + 3/5) - 19637500*log(x + 2/3
)

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GIAC/XCAS [A]  time = 0.20617, size = 95, normalized size = 0.94 \[ \frac{238595625000 \, x^{7} + 1089586687500 \, x^{6} + 2131807725000 \, x^{5} + 2316445391250 \, x^{4} + 1509746867100 \, x^{3} + 590188362770 \, x^{2} + 128130976648 \, x + 11917538647}{10 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{6}} + 19637500 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 19637500 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/10*(238595625000*x^7 + 1089586687500*x^6 + 2131807725000*x^5 + 2316445391250*x
^4 + 1509746867100*x^3 + 590188362770*x^2 + 128130976648*x + 11917538647)/((5*x
+ 3)^2*(3*x + 2)^6) + 19637500*ln(abs(5*x + 3)) - 19637500*ln(abs(3*x + 2))