3.1451 \(\int \frac{(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx\)

Optimal. Leaf size=79 \[ -\frac{54675 x^{10}}{4}-\frac{423225 x^9}{4}-\frac{24381405 x^8}{64}-\frac{95297877 x^7}{112}-\frac{85228263 x^6}{64}-\frac{504354357 x^5}{320}-\frac{772025397 x^4}{512}-\frac{969544757 x^3}{768}-\frac{1065169973 x^2}{1024}-\frac{1092596789 x}{1024}-\frac{1096135733 \log (1-2 x)}{2048} \]

[Out]

(-1092596789*x)/1024 - (1065169973*x^2)/1024 - (969544757*x^3)/768 - (772025397*
x^4)/512 - (504354357*x^5)/320 - (85228263*x^6)/64 - (95297877*x^7)/112 - (24381
405*x^8)/64 - (423225*x^9)/4 - (54675*x^10)/4 - (1096135733*Log[1 - 2*x])/2048

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Rubi [A]  time = 0.0787904, antiderivative size = 79, 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 \[ -\frac{54675 x^{10}}{4}-\frac{423225 x^9}{4}-\frac{24381405 x^8}{64}-\frac{95297877 x^7}{112}-\frac{85228263 x^6}{64}-\frac{504354357 x^5}{320}-\frac{772025397 x^4}{512}-\frac{969544757 x^3}{768}-\frac{1065169973 x^2}{1024}-\frac{1092596789 x}{1024}-\frac{1096135733 \log (1-2 x)}{2048} \]

Antiderivative was successfully verified.

[In]  Int[((2 + 3*x)^7*(3 + 5*x)^3)/(1 - 2*x),x]

[Out]

(-1092596789*x)/1024 - (1065169973*x^2)/1024 - (969544757*x^3)/768 - (772025397*
x^4)/512 - (504354357*x^5)/320 - (85228263*x^6)/64 - (95297877*x^7)/112 - (24381
405*x^8)/64 - (423225*x^9)/4 - (54675*x^10)/4 - (1096135733*Log[1 - 2*x])/2048

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{54675 x^{10}}{4} - \frac{423225 x^{9}}{4} - \frac{24381405 x^{8}}{64} - \frac{95297877 x^{7}}{112} - \frac{85228263 x^{6}}{64} - \frac{504354357 x^{5}}{320} - \frac{772025397 x^{4}}{512} - \frac{969544757 x^{3}}{768} - \frac{1096135733 \log{\left (- 2 x + 1 \right )}}{2048} + \int \left (- \frac{1092596789}{1024}\right )\, dx - \frac{1065169973 \int x\, dx}{512} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**7*(3+5*x)**3/(1-2*x),x)

[Out]

-54675*x**10/4 - 423225*x**9/4 - 24381405*x**8/64 - 95297877*x**7/112 - 85228263
*x**6/64 - 504354357*x**5/320 - 772025397*x**4/512 - 969544757*x**3/768 - 109613
5733*log(-2*x + 1)/2048 + Integral(-1092596789/1024, x) - 1065169973*Integral(x,
x)/512

_______________________________________________________________________________________

Mathematica [A]  time = 0.0240051, size = 82, normalized size = 1.04 \[ -\frac{54675 x^{10}}{4}-\frac{423225 x^9}{4}-\frac{24381405 x^8}{64}-\frac{95297877 x^7}{112}-\frac{85228263 x^6}{64}-\frac{504354357 x^5}{320}-\frac{772025397 x^4}{512}-\frac{969544757 x^3}{768}-\frac{1065169973 x^2}{1024}-\frac{1092596789 x}{1024}-\frac{1096135733 \log (1-2 x)}{2048}+\frac{1933652224451}{1720320} \]

Antiderivative was successfully verified.

[In]  Integrate[((2 + 3*x)^7*(3 + 5*x)^3)/(1 - 2*x),x]

[Out]

1933652224451/1720320 - (1092596789*x)/1024 - (1065169973*x^2)/1024 - (969544757
*x^3)/768 - (772025397*x^4)/512 - (504354357*x^5)/320 - (85228263*x^6)/64 - (952
97877*x^7)/112 - (24381405*x^8)/64 - (423225*x^9)/4 - (54675*x^10)/4 - (10961357
33*Log[1 - 2*x])/2048

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Maple [A]  time = 0.004, size = 58, normalized size = 0.7 \[ -{\frac{54675\,{x}^{10}}{4}}-{\frac{423225\,{x}^{9}}{4}}-{\frac{24381405\,{x}^{8}}{64}}-{\frac{95297877\,{x}^{7}}{112}}-{\frac{85228263\,{x}^{6}}{64}}-{\frac{504354357\,{x}^{5}}{320}}-{\frac{772025397\,{x}^{4}}{512}}-{\frac{969544757\,{x}^{3}}{768}}-{\frac{1065169973\,{x}^{2}}{1024}}-{\frac{1092596789\,x}{1024}}-{\frac{1096135733\,\ln \left ( -1+2\,x \right ) }{2048}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^7*(3+5*x)^3/(1-2*x),x)

[Out]

-54675/4*x^10-423225/4*x^9-24381405/64*x^8-95297877/112*x^7-85228263/64*x^6-5043
54357/320*x^5-772025397/512*x^4-969544757/768*x^3-1065169973/1024*x^2-1092596789
/1024*x-1096135733/2048*ln(-1+2*x)

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Maxima [A]  time = 1.33766, size = 77, normalized size = 0.97 \[ -\frac{54675}{4} \, x^{10} - \frac{423225}{4} \, x^{9} - \frac{24381405}{64} \, x^{8} - \frac{95297877}{112} \, x^{7} - \frac{85228263}{64} \, x^{6} - \frac{504354357}{320} \, x^{5} - \frac{772025397}{512} \, x^{4} - \frac{969544757}{768} \, x^{3} - \frac{1065169973}{1024} \, x^{2} - \frac{1092596789}{1024} \, x - \frac{1096135733}{2048} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^7/(2*x - 1),x, algorithm="maxima")

[Out]

-54675/4*x^10 - 423225/4*x^9 - 24381405/64*x^8 - 95297877/112*x^7 - 85228263/64*
x^6 - 504354357/320*x^5 - 772025397/512*x^4 - 969544757/768*x^3 - 1065169973/102
4*x^2 - 1092596789/1024*x - 1096135733/2048*log(2*x - 1)

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Fricas [A]  time = 0.221967, size = 77, normalized size = 0.97 \[ -\frac{54675}{4} \, x^{10} - \frac{423225}{4} \, x^{9} - \frac{24381405}{64} \, x^{8} - \frac{95297877}{112} \, x^{7} - \frac{85228263}{64} \, x^{6} - \frac{504354357}{320} \, x^{5} - \frac{772025397}{512} \, x^{4} - \frac{969544757}{768} \, x^{3} - \frac{1065169973}{1024} \, x^{2} - \frac{1092596789}{1024} \, x - \frac{1096135733}{2048} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^7/(2*x - 1),x, algorithm="fricas")

[Out]

-54675/4*x^10 - 423225/4*x^9 - 24381405/64*x^8 - 95297877/112*x^7 - 85228263/64*
x^6 - 504354357/320*x^5 - 772025397/512*x^4 - 969544757/768*x^3 - 1065169973/102
4*x^2 - 1092596789/1024*x - 1096135733/2048*log(2*x - 1)

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Sympy [A]  time = 0.248008, size = 76, normalized size = 0.96 \[ - \frac{54675 x^{10}}{4} - \frac{423225 x^{9}}{4} - \frac{24381405 x^{8}}{64} - \frac{95297877 x^{7}}{112} - \frac{85228263 x^{6}}{64} - \frac{504354357 x^{5}}{320} - \frac{772025397 x^{4}}{512} - \frac{969544757 x^{3}}{768} - \frac{1065169973 x^{2}}{1024} - \frac{1092596789 x}{1024} - \frac{1096135733 \log{\left (2 x - 1 \right )}}{2048} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**7*(3+5*x)**3/(1-2*x),x)

[Out]

-54675*x**10/4 - 423225*x**9/4 - 24381405*x**8/64 - 95297877*x**7/112 - 85228263
*x**6/64 - 504354357*x**5/320 - 772025397*x**4/512 - 969544757*x**3/768 - 106516
9973*x**2/1024 - 1092596789*x/1024 - 1096135733*log(2*x - 1)/2048

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.21134, size = 78, normalized size = 0.99 \[ -\frac{54675}{4} \, x^{10} - \frac{423225}{4} \, x^{9} - \frac{24381405}{64} \, x^{8} - \frac{95297877}{112} \, x^{7} - \frac{85228263}{64} \, x^{6} - \frac{504354357}{320} \, x^{5} - \frac{772025397}{512} \, x^{4} - \frac{969544757}{768} \, x^{3} - \frac{1065169973}{1024} \, x^{2} - \frac{1092596789}{1024} \, x - \frac{1096135733}{2048} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^7/(2*x - 1),x, algorithm="giac")

[Out]

-54675/4*x^10 - 423225/4*x^9 - 24381405/64*x^8 - 95297877/112*x^7 - 85228263/64*
x^6 - 504354357/320*x^5 - 772025397/512*x^4 - 969544757/768*x^3 - 1065169973/102
4*x^2 - 1092596789/1024*x - 1096135733/2048*ln(abs(2*x - 1))