3.1605 \(\int \frac{(2+3 x)^3}{(1-2 x)^2 (3+5 x)^3} \, dx\)

Optimal. Leaf size=54 \[ \frac{343}{2662 (1-2 x)}-\frac{103}{33275 (5 x+3)}-\frac{1}{6050 (5 x+3)^2}-\frac{147 \log (1-2 x)}{14641}+\frac{147 \log (5 x+3)}{14641} \]

[Out]

343/(2662*(1 - 2*x)) - 1/(6050*(3 + 5*x)^2) - 103/(33275*(3 + 5*x)) - (147*Log[1
- 2*x])/14641 + (147*Log[3 + 5*x])/14641

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Rubi [A]  time = 0.063548, antiderivative size = 54, 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 \[ \frac{343}{2662 (1-2 x)}-\frac{103}{33275 (5 x+3)}-\frac{1}{6050 (5 x+3)^2}-\frac{147 \log (1-2 x)}{14641}+\frac{147 \log (5 x+3)}{14641} \]

Antiderivative was successfully verified.

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

[Out]

343/(2662*(1 - 2*x)) - 1/(6050*(3 + 5*x)^2) - 103/(33275*(3 + 5*x)) - (147*Log[1
- 2*x])/14641 + (147*Log[3 + 5*x])/14641

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Rubi in Sympy [A]  time = 8.9127, size = 42, normalized size = 0.78 \[ - \frac{147 \log{\left (- 2 x + 1 \right )}}{14641} + \frac{147 \log{\left (5 x + 3 \right )}}{14641} - \frac{103}{33275 \left (5 x + 3\right )} - \frac{1}{6050 \left (5 x + 3\right )^{2}} + \frac{343}{2662 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-147*log(-2*x + 1)/14641 + 147*log(5*x + 3)/14641 - 103/(33275*(5*x + 3)) - 1/(6
050*(5*x + 3)**2) + 343/(2662*(-2*x + 1))

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Mathematica [A]  time = 0.0446536, size = 47, normalized size = 0.87 \[ \frac{-\frac{11 \left (216435 x^2+257478 x+76546\right )}{(2 x-1) (5 x+3)^2}-7350 \log (1-2 x)+7350 \log (10 x+6)}{732050} \]

Antiderivative was successfully verified.

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

[Out]

((-11*(76546 + 257478*x + 216435*x^2))/((-1 + 2*x)*(3 + 5*x)^2) - 7350*Log[1 - 2
*x] + 7350*Log[6 + 10*x])/732050

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Maple [A]  time = 0.015, size = 45, normalized size = 0.8 \[ -{\frac{1}{6050\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{103}{99825+166375\,x}}+{\frac{147\,\ln \left ( 3+5\,x \right ) }{14641}}-{\frac{343}{-2662+5324\,x}}-{\frac{147\,\ln \left ( -1+2\,x \right ) }{14641}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6050/(3+5*x)^2-103/33275/(3+5*x)+147/14641*ln(3+5*x)-343/2662/(-1+2*x)-147/14
641*ln(-1+2*x)

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Maxima [A]  time = 1.34805, size = 62, normalized size = 1.15 \[ -\frac{216435 \, x^{2} + 257478 \, x + 76546}{66550 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac{147}{14641} \, \log \left (5 \, x + 3\right ) - \frac{147}{14641} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/66550*(216435*x^2 + 257478*x + 76546)/(50*x^3 + 35*x^2 - 12*x - 9) + 147/1464
1*log(5*x + 3) - 147/14641*log(2*x - 1)

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Fricas [A]  time = 0.218522, size = 101, normalized size = 1.87 \[ -\frac{2380785 \, x^{2} - 7350 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 7350 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) + 2832258 \, x + 842006}{732050 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/732050*(2380785*x^2 - 7350*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) + 7350*(
50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) + 2832258*x + 842006)/(50*x^3 + 35*x^2
- 12*x - 9)

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Sympy [A]  time = 0.395238, size = 44, normalized size = 0.81 \[ - \frac{216435 x^{2} + 257478 x + 76546}{3327500 x^{3} + 2329250 x^{2} - 798600 x - 598950} - \frac{147 \log{\left (x - \frac{1}{2} \right )}}{14641} + \frac{147 \log{\left (x + \frac{3}{5} \right )}}{14641} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(216435*x**2 + 257478*x + 76546)/(3327500*x**3 + 2329250*x**2 - 798600*x - 5989
50) - 147*log(x - 1/2)/14641 + 147*log(x + 3/5)/14641

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GIAC/XCAS [A]  time = 0.207301, size = 69, normalized size = 1.28 \[ -\frac{343}{2662 \,{\left (2 \, x - 1\right )}} + \frac{2 \,{\left (\frac{231}{2 \, x - 1} + 104\right )}}{14641 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}} + \frac{147}{14641} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-343/2662/(2*x - 1) + 2/14641*(231/(2*x - 1) + 104)/(11/(2*x - 1) + 5)^2 + 147/1
4641*ln(abs(-11/(2*x - 1) - 5))