3.1201 \(\int \frac{1-2 x}{(2+3 x)^4 (3+5 x)^2} \, dx\)

Optimal. Leaf size=55 \[ -\frac{505}{3 x+2}-\frac{275}{5 x+3}-\frac{34}{(3 x+2)^2}-\frac{7}{3 (3 x+2)^3}+3350 \log (3 x+2)-3350 \log (5 x+3) \]

[Out]

-7/(3*(2 + 3*x)^3) - 34/(2 + 3*x)^2 - 505/(2 + 3*x) - 275/(3 + 5*x) + 3350*Log[2
+ 3*x] - 3350*Log[3 + 5*x]

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Rubi [A]  time = 0.0644043, antiderivative size = 55, 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 \[ -\frac{505}{3 x+2}-\frac{275}{5 x+3}-\frac{34}{(3 x+2)^2}-\frac{7}{3 (3 x+2)^3}+3350 \log (3 x+2)-3350 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)^2),x]

[Out]

-7/(3*(2 + 3*x)^3) - 34/(2 + 3*x)^2 - 505/(2 + 3*x) - 275/(3 + 5*x) + 3350*Log[2
+ 3*x] - 3350*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 9.0296, size = 48, normalized size = 0.87 \[ 3350 \log{\left (3 x + 2 \right )} - 3350 \log{\left (5 x + 3 \right )} - \frac{275}{5 x + 3} - \frac{505}{3 x + 2} - \frac{34}{\left (3 x + 2\right )^{2}} - \frac{7}{3 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)/(2+3*x)**4/(3+5*x)**2,x)

[Out]

3350*log(3*x + 2) - 3350*log(5*x + 3) - 275/(5*x + 3) - 505/(3*x + 2) - 34/(3*x
+ 2)**2 - 7/(3*(3*x + 2)**3)

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Mathematica [A]  time = 0.0317826, size = 57, normalized size = 1.04 \[ -\frac{505}{3 x+2}-\frac{275}{5 x+3}-\frac{34}{(3 x+2)^2}-\frac{7}{3 (3 x+2)^3}+3350 \log (3 x+2)-3350 \log (-3 (5 x+3)) \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)/((2 + 3*x)^4*(3 + 5*x)^2),x]

[Out]

-7/(3*(2 + 3*x)^3) - 34/(2 + 3*x)^2 - 505/(2 + 3*x) - 275/(3 + 5*x) + 3350*Log[2
+ 3*x] - 3350*Log[-3*(3 + 5*x)]

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Maple [A]  time = 0.016, size = 54, normalized size = 1. \[ -{\frac{7}{3\, \left ( 2+3\,x \right ) ^{3}}}-34\, \left ( 2+3\,x \right ) ^{-2}-505\, \left ( 2+3\,x \right ) ^{-1}-275\, \left ( 3+5\,x \right ) ^{-1}+3350\,\ln \left ( 2+3\,x \right ) -3350\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)/(2+3*x)^4/(3+5*x)^2,x)

[Out]

-7/3/(2+3*x)^3-34/(2+3*x)^2-505/(2+3*x)-275/(3+5*x)+3350*ln(2+3*x)-3350*ln(3+5*x
)

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Maxima [A]  time = 1.34009, size = 76, normalized size = 1.38 \[ -\frac{90450 \, x^{3} + 177885 \, x^{2} + 116513 \, x + 25413}{3 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} - 3350 \, \log \left (5 \, x + 3\right ) + 3350 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x - 1)/((5*x + 3)^2*(3*x + 2)^4),x, algorithm="maxima")

[Out]

-1/3*(90450*x^3 + 177885*x^2 + 116513*x + 25413)/(135*x^4 + 351*x^3 + 342*x^2 +
148*x + 24) - 3350*log(5*x + 3) + 3350*log(3*x + 2)

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Fricas [A]  time = 0.233625, size = 128, normalized size = 2.33 \[ -\frac{90450 \, x^{3} + 177885 \, x^{2} + 10050 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (5 \, x + 3\right ) - 10050 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (3 \, x + 2\right ) + 116513 \, x + 25413}{3 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x - 1)/((5*x + 3)^2*(3*x + 2)^4),x, algorithm="fricas")

[Out]

-1/3*(90450*x^3 + 177885*x^2 + 10050*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*
log(5*x + 3) - 10050*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(3*x + 2) + 1
16513*x + 25413)/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)

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Sympy [A]  time = 0.418224, size = 51, normalized size = 0.93 \[ - \frac{90450 x^{3} + 177885 x^{2} + 116513 x + 25413}{405 x^{4} + 1053 x^{3} + 1026 x^{2} + 444 x + 72} - 3350 \log{\left (x + \frac{3}{5} \right )} + 3350 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)/(2+3*x)**4/(3+5*x)**2,x)

[Out]

-(90450*x**3 + 177885*x**2 + 116513*x + 25413)/(405*x**4 + 1053*x**3 + 1026*x**2
+ 444*x + 72) - 3350*log(x + 3/5) + 3350*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.207674, size = 78, normalized size = 1.42 \[ -\frac{275}{5 \, x + 3} + \frac{225 \,{\left (\frac{339}{5 \, x + 3} + \frac{68}{{\left (5 \, x + 3\right )}^{2}} + 440\right )}}{{\left (\frac{1}{5 \, x + 3} + 3\right )}^{3}} + 3350 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x - 1)/((5*x + 3)^2*(3*x + 2)^4),x, algorithm="giac")

[Out]

-275/(5*x + 3) + 225*(339/(5*x + 3) + 68/(5*x + 3)^2 + 440)/(1/(5*x + 3) + 3)^3
+ 3350*ln(abs(-1/(5*x + 3) - 3))