3.1468 \(\int \frac{(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx\)

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 - (24381405*x^8)/64 - (423225*x^9)/4 - (54675*x^10)/4 - (1096135733*
Log[1 - 2*x])/2048

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Rubi [A]  time = 0.0387576, 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, Rules used = {88} \[ -\frac{54675 x^{10}}{4}-\frac{423225 x^9}{4}-\frac{24381405 x^8}{64}-\frac{95297877 x^7}{112}-\frac{85228263 x^6}{64}-\frac{504354357 x^5}{320}-\frac{772025397 x^4}{512}-\frac{969544757 x^3}{768}-\frac{1065169973 x^2}{1024}-\frac{1092596789 x}{1024}-\frac{1096135733 \log (1-2 x)}{2048} \]

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 - (24381405*x^8)/64 - (423225*x^9)/4 - (54675*x^10)/4 - (1096135733*
Log[1 - 2*x])/2048

Rule 88

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps

\begin{align*} \int \frac{(2+3 x)^7 (3+5 x)^3}{1-2 x} \, dx &=\int \left (-\frac{1092596789}{1024}-\frac{1065169973 x}{512}-\frac{969544757 x^2}{256}-\frac{772025397 x^3}{128}-\frac{504354357 x^4}{64}-\frac{255684789 x^5}{32}-\frac{95297877 x^6}{16}-\frac{24381405 x^7}{8}-\frac{3809025 x^8}{4}-\frac{273375 x^9}{2}-\frac{1096135733}{1024 (-1+2 x)}\right ) \, dx\\ &=-\frac{1092596789 x}{1024}-\frac{1065169973 x^2}{1024}-\frac{969544757 x^3}{768}-\frac{772025397 x^4}{512}-\frac{504354357 x^5}{320}-\frac{85228263 x^6}{64}-\frac{95297877 x^7}{112}-\frac{24381405 x^8}{64}-\frac{423225 x^9}{4}-\frac{54675 x^{10}}{4}-\frac{1096135733 \log (1-2 x)}{2048}\\ \end{align*}

Mathematica [A]  time = 0.0147742, 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)/51
2 - (504354357*x^5)/320 - (85228263*x^6)/64 - (95297877*x^7)/112 - (24381405*x^8)/64 - (423225*x^9)/4 - (54675
*x^10)/4 - (1096135733*Log[1 - 2*x])/2048

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Maple [A]  time = 0.004, size = 58, normalized size = 0.7 \begin{align*} -{\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 ( 2\,x-1 \right ) }{2048}} \end{align*}

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^6-504354357/320*x^5-772025397/512*x^
4-969544757/768*x^3-1065169973/1024*x^2-1092596789/1024*x-1096135733/2048*ln(2*x-1)

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Maxima [A]  time = 1.0631, size = 77, normalized size = 0.97 \begin{align*} -\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 ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^7*(3+5*x)^3/(1-2*x),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 - 7720
25397/512*x^4 - 969544757/768*x^3 - 1065169973/1024*x^2 - 1092596789/1024*x - 1096135733/2048*log(2*x - 1)

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Fricas [A]  time = 1.27228, size = 294, normalized size = 3.72 \begin{align*} -\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 ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^7*(3+5*x)^3/(1-2*x),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 - 7720
25397/512*x^4 - 969544757/768*x^3 - 1065169973/1024*x^2 - 1092596789/1024*x - 1096135733/2048*log(2*x - 1)

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Sympy [A]  time = 0.112532, size = 76, normalized size = 0.96 \begin{align*} - \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} \end{align*}

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 - 1065169973*x**2/1024 - 1092596789*x/1024 - 1096135733*log(2*x - 1)
/2048

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Giac [A]  time = 1.29538, size = 78, normalized size = 0.99 \begin{align*} -\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 ({\left | 2 \, x - 1 \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^7*(3+5*x)^3/(1-2*x),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 - 7720
25397/512*x^4 - 969544757/768*x^3 - 1065169973/1024*x^2 - 1092596789/1024*x - 1096135733/2048*log(abs(2*x - 1)
)