3.1607 \(\int \frac{2+3 x}{(1-2 x)^2 (3+5 x)^3} \, dx\)

Optimal. Leaf size=54 \[ \frac{14}{1331 (1-2 x)}-\frac{37}{1331 (5 x+3)}-\frac{1}{242 (5 x+3)^2}-\frac{144 \log (1-2 x)}{14641}+\frac{144 \log (5 x+3)}{14641} \]

[Out]

14/(1331*(1 - 2*x)) - 1/(242*(3 + 5*x)^2) - 37/(1331*(3 + 5*x)) - (144*Log[1 - 2
*x])/14641 + (144*Log[3 + 5*x])/14641

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Rubi [A]  time = 0.0569679, antiderivative size = 54, 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 \[ \frac{14}{1331 (1-2 x)}-\frac{37}{1331 (5 x+3)}-\frac{1}{242 (5 x+3)^2}-\frac{144 \log (1-2 x)}{14641}+\frac{144 \log (5 x+3)}{14641} \]

Antiderivative was successfully verified.

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

[Out]

14/(1331*(1 - 2*x)) - 1/(242*(3 + 5*x)^2) - 37/(1331*(3 + 5*x)) - (144*Log[1 - 2
*x])/14641 + (144*Log[3 + 5*x])/14641

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Rubi in Sympy [A]  time = 8.4943, size = 42, normalized size = 0.78 \[ - \frac{144 \log{\left (- 2 x + 1 \right )}}{14641} + \frac{144 \log{\left (5 x + 3 \right )}}{14641} - \frac{37}{1331 \left (5 x + 3\right )} - \frac{1}{242 \left (5 x + 3\right )^{2}} + \frac{14}{1331 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-144*log(-2*x + 1)/14641 + 144*log(5*x + 3)/14641 - 37/(1331*(5*x + 3)) - 1/(242
*(5*x + 3)**2) + 14/(1331*(-2*x + 1))

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Mathematica [A]  time = 0.0402459, size = 47, normalized size = 0.87 \[ \frac{-\frac{11 \left (1440 x^2+936 x+19\right )}{(2 x-1) (5 x+3)^2}-288 \log (1-2 x)+288 \log (10 x+6)}{29282} \]

Antiderivative was successfully verified.

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

[Out]

((-11*(19 + 936*x + 1440*x^2))/((-1 + 2*x)*(3 + 5*x)^2) - 288*Log[1 - 2*x] + 288
*Log[6 + 10*x])/29282

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Maple [A]  time = 0.014, size = 45, normalized size = 0.8 \[ -{\frac{1}{242\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{37}{3993+6655\,x}}+{\frac{144\,\ln \left ( 3+5\,x \right ) }{14641}}-{\frac{14}{-1331+2662\,x}}-{\frac{144\,\ln \left ( -1+2\,x \right ) }{14641}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/242/(3+5*x)^2-37/1331/(3+5*x)+144/14641*ln(3+5*x)-14/1331/(-1+2*x)-144/14641*
ln(-1+2*x)

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Maxima [A]  time = 1.34548, size = 62, normalized size = 1.15 \[ -\frac{1440 \, x^{2} + 936 \, x + 19}{2662 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac{144}{14641} \, \log \left (5 \, x + 3\right ) - \frac{144}{14641} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2662*(1440*x^2 + 936*x + 19)/(50*x^3 + 35*x^2 - 12*x - 9) + 144/14641*log(5*x
+ 3) - 144/14641*log(2*x - 1)

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Fricas [A]  time = 0.216425, size = 101, normalized size = 1.87 \[ -\frac{15840 \, x^{2} - 288 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 288 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) + 10296 \, x + 209}{29282 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/29282*(15840*x^2 - 288*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) + 288*(50*x^
3 + 35*x^2 - 12*x - 9)*log(2*x - 1) + 10296*x + 209)/(50*x^3 + 35*x^2 - 12*x - 9
)

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Sympy [A]  time = 0.370189, size = 44, normalized size = 0.81 \[ - \frac{1440 x^{2} + 936 x + 19}{133100 x^{3} + 93170 x^{2} - 31944 x - 23958} - \frac{144 \log{\left (x - \frac{1}{2} \right )}}{14641} + \frac{144 \log{\left (x + \frac{3}{5} \right )}}{14641} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(1440*x**2 + 936*x + 19)/(133100*x**3 + 93170*x**2 - 31944*x - 23958) - 144*log
(x - 1/2)/14641 + 144*log(x + 3/5)/14641

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GIAC/XCAS [A]  time = 0.20531, size = 69, normalized size = 1.28 \[ -\frac{14}{1331 \,{\left (2 \, x - 1\right )}} + \frac{10 \,{\left (\frac{429}{2 \, x - 1} + 190\right )}}{14641 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}} + \frac{144}{14641} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-14/1331/(2*x - 1) + 10/14641*(429/(2*x - 1) + 190)/(11/(2*x - 1) + 5)^2 + 144/1
4641*ln(abs(-11/(2*x - 1) - 5))