3.1455 \(\int \frac{(2+3 x)^3 (3+5 x)^3}{1-2 x} \, dx\)

Optimal. Leaf size=51 \[ -\frac{1125 x^6}{4}-\frac{5805 x^5}{4}-\frac{110205 x^4}{32}-\frac{247157 x^3}{48}-\frac{377045 x^2}{64}-\frac{442709 x}{64}-\frac{456533}{128} \log (1-2 x) \]

[Out]

(-442709*x)/64 - (377045*x^2)/64 - (247157*x^3)/48 - (110205*x^4)/32 - (5805*x^5
)/4 - (1125*x^6)/4 - (456533*Log[1 - 2*x])/128

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Rubi [A]  time = 0.0538503, antiderivative size = 51, 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 \[ -\frac{1125 x^6}{4}-\frac{5805 x^5}{4}-\frac{110205 x^4}{32}-\frac{247157 x^3}{48}-\frac{377045 x^2}{64}-\frac{442709 x}{64}-\frac{456533}{128} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

(-442709*x)/64 - (377045*x^2)/64 - (247157*x^3)/48 - (110205*x^4)/32 - (5805*x^5
)/4 - (1125*x^6)/4 - (456533*Log[1 - 2*x])/128

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{1125 x^{6}}{4} - \frac{5805 x^{5}}{4} - \frac{110205 x^{4}}{32} - \frac{247157 x^{3}}{48} - \frac{456533 \log{\left (- 2 x + 1 \right )}}{128} + \int \left (- \frac{442709}{64}\right )\, dx - \frac{377045 \int x\, dx}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1125*x**6/4 - 5805*x**5/4 - 110205*x**4/32 - 247157*x**3/48 - 456533*log(-2*x +
1)/128 + Integral(-442709/64, x) - 377045*Integral(x, x)/32

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Mathematica [A]  time = 0.0176746, size = 42, normalized size = 0.82 \[ \frac{-432000 x^6-2229120 x^5-5289840 x^4-7909024 x^3-9049080 x^2-10625016 x-5478396 \log (1-2 x)+8970431}{1536} \]

Antiderivative was successfully verified.

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

[Out]

(8970431 - 10625016*x - 9049080*x^2 - 7909024*x^3 - 5289840*x^4 - 2229120*x^5 -
432000*x^6 - 5478396*Log[1 - 2*x])/1536

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Maple [A]  time = 0.003, size = 38, normalized size = 0.8 \[ -{\frac{1125\,{x}^{6}}{4}}-{\frac{5805\,{x}^{5}}{4}}-{\frac{110205\,{x}^{4}}{32}}-{\frac{247157\,{x}^{3}}{48}}-{\frac{377045\,{x}^{2}}{64}}-{\frac{442709\,x}{64}}-{\frac{456533\,\ln \left ( -1+2\,x \right ) }{128}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1125/4*x^6-5805/4*x^5-110205/32*x^4-247157/48*x^3-377045/64*x^2-442709/64*x-456
533/128*ln(-1+2*x)

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Maxima [A]  time = 1.35741, size = 50, normalized size = 0.98 \[ -\frac{1125}{4} \, x^{6} - \frac{5805}{4} \, x^{5} - \frac{110205}{32} \, x^{4} - \frac{247157}{48} \, x^{3} - \frac{377045}{64} \, x^{2} - \frac{442709}{64} \, x - \frac{456533}{128} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1125/4*x^6 - 5805/4*x^5 - 110205/32*x^4 - 247157/48*x^3 - 377045/64*x^2 - 44270
9/64*x - 456533/128*log(2*x - 1)

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Fricas [A]  time = 0.218901, size = 50, normalized size = 0.98 \[ -\frac{1125}{4} \, x^{6} - \frac{5805}{4} \, x^{5} - \frac{110205}{32} \, x^{4} - \frac{247157}{48} \, x^{3} - \frac{377045}{64} \, x^{2} - \frac{442709}{64} \, x - \frac{456533}{128} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1125/4*x^6 - 5805/4*x^5 - 110205/32*x^4 - 247157/48*x^3 - 377045/64*x^2 - 44270
9/64*x - 456533/128*log(2*x - 1)

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Sympy [A]  time = 0.203464, size = 49, normalized size = 0.96 \[ - \frac{1125 x^{6}}{4} - \frac{5805 x^{5}}{4} - \frac{110205 x^{4}}{32} - \frac{247157 x^{3}}{48} - \frac{377045 x^{2}}{64} - \frac{442709 x}{64} - \frac{456533 \log{\left (2 x - 1 \right )}}{128} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1125*x**6/4 - 5805*x**5/4 - 110205*x**4/32 - 247157*x**3/48 - 377045*x**2/64 -
442709*x/64 - 456533*log(2*x - 1)/128

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GIAC/XCAS [A]  time = 0.208944, size = 51, normalized size = 1. \[ -\frac{1125}{4} \, x^{6} - \frac{5805}{4} \, x^{5} - \frac{110205}{32} \, x^{4} - \frac{247157}{48} \, x^{3} - \frac{377045}{64} \, x^{2} - \frac{442709}{64} \, x - \frac{456533}{128} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1125/4*x^6 - 5805/4*x^5 - 110205/32*x^4 - 247157/48*x^3 - 377045/64*x^2 - 44270
9/64*x - 456533/128*ln(abs(2*x - 1))