3.1470 \(\int \frac{(2+3 x)^6}{(1-2 x) (3+5 x)} \, dx\)

Optimal. Leaf size=54 \[ -\frac{729 x^5}{50}-\frac{28431 x^4}{400}-\frac{159813 x^3}{1000}-\frac{4693491 x^2}{20000}-\frac{31289679 x}{100000}-\frac{117649}{704} \log (1-2 x)+\frac{\log (5 x+3)}{171875} \]

[Out]

(-31289679*x)/100000 - (4693491*x^2)/20000 - (159813*x^3)/1000 - (28431*x^4)/400
- (729*x^5)/50 - (117649*Log[1 - 2*x])/704 + Log[3 + 5*x]/171875

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Rubi [A]  time = 0.0581985, 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 \[ -\frac{729 x^5}{50}-\frac{28431 x^4}{400}-\frac{159813 x^3}{1000}-\frac{4693491 x^2}{20000}-\frac{31289679 x}{100000}-\frac{117649}{704} \log (1-2 x)+\frac{\log (5 x+3)}{171875} \]

Antiderivative was successfully verified.

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

[Out]

(-31289679*x)/100000 - (4693491*x^2)/20000 - (159813*x^3)/1000 - (28431*x^4)/400
- (729*x^5)/50 - (117649*Log[1 - 2*x])/704 + Log[3 + 5*x]/171875

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{729 x^{5}}{50} - \frac{28431 x^{4}}{400} - \frac{159813 x^{3}}{1000} - \frac{117649 \log{\left (- 2 x + 1 \right )}}{704} + \frac{\log{\left (5 x + 3 \right )}}{171875} + \int \left (- \frac{31289679}{100000}\right )\, dx - \frac{4693491 \int x\, dx}{10000} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-729*x**5/50 - 28431*x**4/400 - 159813*x**3/1000 - 117649*log(-2*x + 1)/704 + lo
g(5*x + 3)/171875 + Integral(-31289679/100000, x) - 4693491*Integral(x, x)/10000

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Mathematica [A]  time = 0.0313129, size = 50, normalized size = 0.93 \[ \frac{-2970 \left (54000 x^5+263250 x^4+591900 x^3+869165 x^2+1158877 x+516778\right )-1838265625 \log (3-6 x)+64 \log (-3 (5 x+3))}{11000000} \]

Antiderivative was successfully verified.

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

[Out]

(-2970*(516778 + 1158877*x + 869165*x^2 + 591900*x^3 + 263250*x^4 + 54000*x^5) -
1838265625*Log[3 - 6*x] + 64*Log[-3*(3 + 5*x)])/11000000

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Maple [A]  time = 0.01, size = 41, normalized size = 0.8 \[ -{\frac{729\,{x}^{5}}{50}}-{\frac{28431\,{x}^{4}}{400}}-{\frac{159813\,{x}^{3}}{1000}}-{\frac{4693491\,{x}^{2}}{20000}}-{\frac{31289679\,x}{100000}}+{\frac{\ln \left ( 3+5\,x \right ) }{171875}}-{\frac{117649\,\ln \left ( -1+2\,x \right ) }{704}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-729/50*x^5-28431/400*x^4-159813/1000*x^3-4693491/20000*x^2-31289679/100000*x+1/
171875*ln(3+5*x)-117649/704*ln(-1+2*x)

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Maxima [A]  time = 1.35134, size = 54, normalized size = 1. \[ -\frac{729}{50} \, x^{5} - \frac{28431}{400} \, x^{4} - \frac{159813}{1000} \, x^{3} - \frac{4693491}{20000} \, x^{2} - \frac{31289679}{100000} \, x + \frac{1}{171875} \, \log \left (5 \, x + 3\right ) - \frac{117649}{704} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-729/50*x^5 - 28431/400*x^4 - 159813/1000*x^3 - 4693491/20000*x^2 - 31289679/100
000*x + 1/171875*log(5*x + 3) - 117649/704*log(2*x - 1)

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Fricas [A]  time = 0.201405, size = 54, normalized size = 1. \[ -\frac{729}{50} \, x^{5} - \frac{28431}{400} \, x^{4} - \frac{159813}{1000} \, x^{3} - \frac{4693491}{20000} \, x^{2} - \frac{31289679}{100000} \, x + \frac{1}{171875} \, \log \left (5 \, x + 3\right ) - \frac{117649}{704} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-729/50*x^5 - 28431/400*x^4 - 159813/1000*x^3 - 4693491/20000*x^2 - 31289679/100
000*x + 1/171875*log(5*x + 3) - 117649/704*log(2*x - 1)

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Sympy [A]  time = 0.305221, size = 49, normalized size = 0.91 \[ - \frac{729 x^{5}}{50} - \frac{28431 x^{4}}{400} - \frac{159813 x^{3}}{1000} - \frac{4693491 x^{2}}{20000} - \frac{31289679 x}{100000} - \frac{117649 \log{\left (x - \frac{1}{2} \right )}}{704} + \frac{\log{\left (x + \frac{3}{5} \right )}}{171875} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-729*x**5/50 - 28431*x**4/400 - 159813*x**3/1000 - 4693491*x**2/20000 - 31289679
*x/100000 - 117649*log(x - 1/2)/704 + log(x + 3/5)/171875

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GIAC/XCAS [A]  time = 0.211884, size = 57, normalized size = 1.06 \[ -\frac{729}{50} \, x^{5} - \frac{28431}{400} \, x^{4} - \frac{159813}{1000} \, x^{3} - \frac{4693491}{20000} \, x^{2} - \frac{31289679}{100000} \, x + \frac{1}{171875} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{117649}{704} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-729/50*x^5 - 28431/400*x^4 - 159813/1000*x^3 - 4693491/20000*x^2 - 31289679/100
000*x + 1/171875*ln(abs(5*x + 3)) - 117649/704*ln(abs(2*x - 1))