3.16.75 \(\int \frac {(2+3 x)^4 (3+5 x)^3}{(1-2 x)^2} \, dx\) [1575]

Optimal. Leaf size=62 \[ \frac {3195731}{256 (1-2 x)}+\frac {209243 x}{4}+\frac {3859469 x^2}{128}+\frac {289951 x^3}{16}+\frac {557415 x^4}{64}+\frac {5535 x^5}{2}+\frac {3375 x^6}{8}+\frac {9836211}{256} \log (1-2 x) \]

[Out]

3195731/256/(1-2*x)+209243/4*x+3859469/128*x^2+289951/16*x^3+557415/64*x^4+5535/2*x^5+3375/8*x^6+9836211/256*l
n(1-2*x)

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Rubi [A]
time = 0.02, antiderivative size = 62, normalized size of antiderivative = 1.00, 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 = {90} \begin {gather*} \frac {3375 x^6}{8}+\frac {5535 x^5}{2}+\frac {557415 x^4}{64}+\frac {289951 x^3}{16}+\frac {3859469 x^2}{128}+\frac {209243 x}{4}+\frac {3195731}{256 (1-2 x)}+\frac {9836211}{256} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^2,x]

[Out]

3195731/(256*(1 - 2*x)) + (209243*x)/4 + (3859469*x^2)/128 + (289951*x^3)/16 + (557415*x^4)/64 + (5535*x^5)/2
+ (3375*x^6)/8 + (9836211*Log[1 - 2*x])/256

Rule 90

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)^4 (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac {209243}{4}+\frac {3859469 x}{64}+\frac {869853 x^2}{16}+\frac {557415 x^3}{16}+\frac {27675 x^4}{2}+\frac {10125 x^5}{4}+\frac {3195731}{128 (-1+2 x)^2}+\frac {9836211}{128 (-1+2 x)}\right ) \, dx\\ &=\frac {3195731}{256 (1-2 x)}+\frac {209243 x}{4}+\frac {3859469 x^2}{128}+\frac {289951 x^3}{16}+\frac {557415 x^4}{64}+\frac {5535 x^5}{2}+\frac {3375 x^6}{8}+\frac {9836211}{256} \log (1-2 x)\\ \end {align*}

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Mathematica [A]
time = 0.01, size = 59, normalized size = 0.95 \begin {gather*} \frac {24691451-128514958 x+76256664 x^2+43194640 x^3+28195088 x^4+15003360 x^5+5235840 x^6+864000 x^7+39344844 (-1+2 x) \log (1-2 x)}{1024 (-1+2 x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^2,x]

[Out]

(24691451 - 128514958*x + 76256664*x^2 + 43194640*x^3 + 28195088*x^4 + 15003360*x^5 + 5235840*x^6 + 864000*x^7
+ 39344844*(-1 + 2*x)*Log[1 - 2*x])/(1024*(-1 + 2*x))

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Maple [A]
time = 0.09, size = 47, normalized size = 0.76

method	result	size
risch	\(\frac {3375 x^{6}}{8}+\frac {5535 x^{5}}{2}+\frac {557415 x^{4}}{64}+\frac {289951 x^{3}}{16}+\frac {3859469 x^{2}}{128}+\frac {209243 x}{4}-\frac {3195731}{512 \left (-\frac {1}{2}+x \right )}+\frac {9836211 \ln \left (-1+2 x \right )}{256}\)	\(45\)
default	\(\frac {3375 x^{6}}{8}+\frac {5535 x^{5}}{2}+\frac {557415 x^{4}}{64}+\frac {289951 x^{3}}{16}+\frac {3859469 x^{2}}{128}+\frac {209243 x}{4}-\frac {3195731}{256 \left (-1+2 x \right )}+\frac {9836211 \ln \left (-1+2 x \right )}{256}\)	\(47\)
norman	\(\frac {-\frac {9891507}{128} x +\frac {9532083}{128} x^{2}+\frac {2699665}{64} x^{3}+\frac {1762193}{64} x^{4}+\frac {468855}{32} x^{5}+\frac {40905}{8} x^{6}+\frac {3375}{4} x^{7}}{-1+2 x}+\frac {9836211 \ln \left (-1+2 x \right )}{256}\)	\(52\)
meijerg	\(\frac {2808 x}{1-2 x}+\frac {9836211 \ln \left (1-2 x \right )}{256}+\frac {1866 x \left (-6 x +6\right )}{1-2 x}+\frac {1831 x \left (-8 x^{2}-12 x +12\right )}{1-2 x}+\frac {30649 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{80 \left (1-2 x \right )}+\frac {28845 x \left (-48 x^{4}-40 x^{3}-40 x^{2}-60 x +60\right )}{128 \left (1-2 x \right )}+\frac {9045 x \left (-448 x^{5}-336 x^{4}-280 x^{3}-280 x^{2}-420 x +420\right )}{896 \left (1-2 x \right )}+\frac {675 x \left (-1280 x^{6}-896 x^{5}-672 x^{4}-560 x^{3}-560 x^{2}-840 x +840\right )}{1024 \left (1-2 x \right )}\)	\(185\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2+3*x)^4*(3+5*x)^3/(1-2*x)^2,x,method=_RETURNVERBOSE)

[Out]

3375/8*x^6+5535/2*x^5+557415/64*x^4+289951/16*x^3+3859469/128*x^2+209243/4*x-3195731/256/(-1+2*x)+9836211/256*
ln(-1+2*x)

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Maxima [A]
time = 0.36, size = 46, normalized size = 0.74 \begin {gather*} \frac {3375}{8} \, x^{6} + \frac {5535}{2} \, x^{5} + \frac {557415}{64} \, x^{4} + \frac {289951}{16} \, x^{3} + \frac {3859469}{128} \, x^{2} + \frac {209243}{4} \, x - \frac {3195731}{256 \, {\left (2 \, x - 1\right )}} + \frac {9836211}{256} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^4*(3+5*x)^3/(1-2*x)^2,x, algorithm="maxima")

[Out]

3375/8*x^6 + 5535/2*x^5 + 557415/64*x^4 + 289951/16*x^3 + 3859469/128*x^2 + 209243/4*x - 3195731/256/(2*x - 1)
+ 9836211/256*log(2*x - 1)

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Fricas [A]
time = 0.65, size = 57, normalized size = 0.92 \begin {gather*} \frac {216000 \, x^{7} + 1308960 \, x^{6} + 3750840 \, x^{5} + 7048772 \, x^{4} + 10798660 \, x^{3} + 19064166 \, x^{2} + 9836211 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 13391552 \, x - 3195731}{256 \, {\left (2 \, x - 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^4*(3+5*x)^3/(1-2*x)^2,x, algorithm="fricas")

[Out]

1/256*(216000*x^7 + 1308960*x^6 + 3750840*x^5 + 7048772*x^4 + 10798660*x^3 + 19064166*x^2 + 9836211*(2*x - 1)*
log(2*x - 1) - 13391552*x - 3195731)/(2*x - 1)

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Sympy [A]
time = 0.04, size = 54, normalized size = 0.87 \begin {gather*} \frac {3375 x^{6}}{8} + \frac {5535 x^{5}}{2} + \frac {557415 x^{4}}{64} + \frac {289951 x^{3}}{16} + \frac {3859469 x^{2}}{128} + \frac {209243 x}{4} + \frac {9836211 \log {\left (2 x - 1 \right )}}{256} - \frac {3195731}{512 x - 256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**4*(3+5*x)**3/(1-2*x)**2,x)

[Out]

3375*x**6/8 + 5535*x**5/2 + 557415*x**4/64 + 289951*x**3/16 + 3859469*x**2/128 + 209243*x/4 + 9836211*log(2*x
- 1)/256 - 3195731/(512*x - 256)

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Giac [A]
time = 0.94, size = 84, normalized size = 1.35 \begin {gather*} \frac {1}{1024} \, {\left (2 \, x - 1\right )}^{6} {\left (\frac {129060}{2 \, x - 1} + \frac {1101465}{{\left (2 \, x - 1\right )}^{2}} + \frac {5569868}{{\left (2 \, x - 1\right )}^{3}} + \frac {19009102}{{\left (2 \, x - 1\right )}^{4}} + \frac {51892764}{{\left (2 \, x - 1\right )}^{5}} + 6750\right )} - \frac {3195731}{256 \, {\left (2 \, x - 1\right )}} - \frac {9836211}{256} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^4*(3+5*x)^3/(1-2*x)^2,x, algorithm="giac")

[Out]

1/1024*(2*x - 1)^6*(129060/(2*x - 1) + 1101465/(2*x - 1)^2 + 5569868/(2*x - 1)^3 + 19009102/(2*x - 1)^4 + 5189
2764/(2*x - 1)^5 + 6750) - 3195731/256/(2*x - 1) - 9836211/256*log(1/2*abs(2*x - 1)/(2*x - 1)^2)

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Mupad [B]
time = 0.04, size = 44, normalized size = 0.71 \begin {gather*} \frac {209243\,x}{4}+\frac {9836211\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {3195731}{512\,\left (x-\frac {1}{2}\right )}+\frac {3859469\,x^2}{128}+\frac {289951\,x^3}{16}+\frac {557415\,x^4}{64}+\frac {5535\,x^5}{2}+\frac {3375\,x^6}{8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3*x + 2)^4*(5*x + 3)^3)/(2*x - 1)^2,x)

[Out]

(209243*x)/4 + (9836211*log(x - 1/2))/256 - 3195731/(512*(x - 1/2)) + (3859469*x^2)/128 + (289951*x^3)/16 + (5
57415*x^4)/64 + (5535*x^5)/2 + (3375*x^6)/8

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