3.1647 \(\int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=45 \[ -\frac{375 x^2}{16}-\frac{2975 x}{16}-\frac{8349}{16 (1-2 x)}+\frac{9317}{64 (1-2 x)^2}-\frac{2805}{8} \log (1-2 x) \]

[Out]

9317/(64*(1 - 2*x)^2) - 8349/(16*(1 - 2*x)) - (2975*x)/16 - (375*x^2)/16 - (2805
*Log[1 - 2*x])/8

_______________________________________________________________________________________

Rubi [A]  time = 0.0552636, antiderivative size = 45, 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 \[ -\frac{375 x^2}{16}-\frac{2975 x}{16}-\frac{8349}{16 (1-2 x)}+\frac{9317}{64 (1-2 x)^2}-\frac{2805}{8} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

9317/(64*(1 - 2*x)^2) - 8349/(16*(1 - 2*x)) - (2975*x)/16 - (375*x^2)/16 - (2805
*Log[1 - 2*x])/8

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{2805 \log{\left (- 2 x + 1 \right )}}{8} + \int \left (- \frac{2975}{16}\right )\, dx - \frac{375 \int x\, dx}{8} - \frac{8349}{16 \left (- 2 x + 1\right )} + \frac{9317}{64 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2805*log(-2*x + 1)/8 + Integral(-2975/16, x) - 375*Integral(x, x)/8 - 8349/(16*
(-2*x + 1)) + 9317/(64*(-2*x + 1)**2)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0228029, size = 46, normalized size = 1.02 \[ -\frac{3000 x^4+20800 x^3-35700 x^2-14796 x+11220 (1-2 x)^2 \log (1-2 x)+8877}{32 (1-2 x)^2} \]

Antiderivative was successfully verified.

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

[Out]

-(8877 - 14796*x - 35700*x^2 + 20800*x^3 + 3000*x^4 + 11220*(1 - 2*x)^2*Log[1 -
2*x])/(32*(1 - 2*x)^2)

_______________________________________________________________________________________

Maple [A]  time = 0.009, size = 36, normalized size = 0.8 \[ -{\frac{375\,{x}^{2}}{16}}-{\frac{2975\,x}{16}}+{\frac{9317}{64\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{8349}{-16+32\,x}}-{\frac{2805\,\ln \left ( -1+2\,x \right ) }{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375/16*x^2-2975/16*x+9317/64/(-1+2*x)^2+8349/16/(-1+2*x)-2805/8*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.35469, size = 49, normalized size = 1.09 \[ -\frac{375}{16} \, x^{2} - \frac{2975}{16} \, x + \frac{121 \,{\left (552 \, x - 199\right )}}{64 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{2805}{8} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375/16*x^2 - 2975/16*x + 121/64*(552*x - 199)/(4*x^2 - 4*x + 1) - 2805/8*log(2*
x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.225577, size = 70, normalized size = 1.56 \[ -\frac{6000 \, x^{4} + 41600 \, x^{3} - 46100 \, x^{2} + 22440 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 54892 \, x + 24079}{64 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/64*(6000*x^4 + 41600*x^3 - 46100*x^2 + 22440*(4*x^2 - 4*x + 1)*log(2*x - 1) -
54892*x + 24079)/(4*x^2 - 4*x + 1)

_______________________________________________________________________________________

Sympy [A]  time = 0.277752, size = 36, normalized size = 0.8 \[ - \frac{375 x^{2}}{16} - \frac{2975 x}{16} + \frac{66792 x - 24079}{256 x^{2} - 256 x + 64} - \frac{2805 \log{\left (2 x - 1 \right )}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375*x**2/16 - 2975*x/16 + (66792*x - 24079)/(256*x**2 - 256*x + 64) - 2805*log(
2*x - 1)/8

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.209548, size = 43, normalized size = 0.96 \[ -\frac{375}{16} \, x^{2} - \frac{2975}{16} \, x + \frac{121 \,{\left (552 \, x - 199\right )}}{64 \,{\left (2 \, x - 1\right )}^{2}} - \frac{2805}{8} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375/16*x^2 - 2975/16*x + 121/64*(552*x - 199)/(2*x - 1)^2 - 2805/8*ln(abs(2*x -
1))