3.1465 \(\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^7} \, dx\)

Optimal. Leaf size=87 \[ -\frac{5324}{117649 (3 x+2)}-\frac{1331}{16807 (3 x+2)^2}-\frac{1331}{7203 (3 x+2)^3}+\frac{3469}{37044 (3 x+2)^4}-\frac{103}{6615 (3 x+2)^5}+\frac{1}{1134 (3 x+2)^6}-\frac{10648 \log (1-2 x)}{823543}+\frac{10648 \log (3 x+2)}{823543} \]

[Out]

1/(1134*(2 + 3*x)^6) - 103/(6615*(2 + 3*x)^5) + 3469/(37044*(2 + 3*x)^4) - 1331/
(7203*(2 + 3*x)^3) - 1331/(16807*(2 + 3*x)^2) - 5324/(117649*(2 + 3*x)) - (10648
*Log[1 - 2*x])/823543 + (10648*Log[2 + 3*x])/823543

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Rubi [A]  time = 0.0856457, antiderivative size = 87, 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 \[ -\frac{5324}{117649 (3 x+2)}-\frac{1331}{16807 (3 x+2)^2}-\frac{1331}{7203 (3 x+2)^3}+\frac{3469}{37044 (3 x+2)^4}-\frac{103}{6615 (3 x+2)^5}+\frac{1}{1134 (3 x+2)^6}-\frac{10648 \log (1-2 x)}{823543}+\frac{10648 \log (3 x+2)}{823543} \]

Antiderivative was successfully verified.

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

[Out]

1/(1134*(2 + 3*x)^6) - 103/(6615*(2 + 3*x)^5) + 3469/(37044*(2 + 3*x)^4) - 1331/
(7203*(2 + 3*x)^3) - 1331/(16807*(2 + 3*x)^2) - 5324/(117649*(2 + 3*x)) - (10648
*Log[1 - 2*x])/823543 + (10648*Log[2 + 3*x])/823543

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Rubi in Sympy [A]  time = 12.8249, size = 76, normalized size = 0.87 \[ - \frac{10648 \log{\left (- 2 x + 1 \right )}}{823543} + \frac{10648 \log{\left (3 x + 2 \right )}}{823543} - \frac{5324}{117649 \left (3 x + 2\right )} - \frac{1331}{16807 \left (3 x + 2\right )^{2}} - \frac{1331}{7203 \left (3 x + 2\right )^{3}} + \frac{3469}{37044 \left (3 x + 2\right )^{4}} - \frac{103}{6615 \left (3 x + 2\right )^{5}} + \frac{1}{1134 \left (3 x + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-10648*log(-2*x + 1)/823543 + 10648*log(3*x + 2)/823543 - 5324/(117649*(3*x + 2)
) - 1331/(16807*(3*x + 2)**2) - 1331/(7203*(3*x + 2)**3) + 3469/(37044*(3*x + 2)
**4) - 103/(6615*(3*x + 2)**5) + 1/(1134*(3*x + 2)**6)

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Mathematica [A]  time = 0.0722925, size = 57, normalized size = 0.66 \[ \frac{4 \left (-\frac{7 \left (2095845840 x^5+8208729540 x^4+13525968060 x^3+11211272235 x^2+4581535248 x+733614062\right )}{16 (3 x+2)^6}-1078110 \log (1-2 x)+1078110 \log (6 x+4)\right )}{333534915} \]

Antiderivative was successfully verified.

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

[Out]

(4*((-7*(733614062 + 4581535248*x + 11211272235*x^2 + 13525968060*x^3 + 82087295
40*x^4 + 2095845840*x^5))/(16*(2 + 3*x)^6) - 1078110*Log[1 - 2*x] + 1078110*Log[
4 + 6*x]))/333534915

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Maple [A]  time = 0.013, size = 72, normalized size = 0.8 \[{\frac{1}{1134\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{103}{6615\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{3469}{37044\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{1331}{7203\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{1331}{16807\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{5324}{235298+352947\,x}}+{\frac{10648\,\ln \left ( 2+3\,x \right ) }{823543}}-{\frac{10648\,\ln \left ( -1+2\,x \right ) }{823543}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1134/(2+3*x)^6-103/6615/(2+3*x)^5+3469/37044/(2+3*x)^4-1331/7203/(2+3*x)^3-133
1/16807/(2+3*x)^2-5324/117649/(2+3*x)+10648/823543*ln(2+3*x)-10648/823543*ln(-1+
2*x)

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Maxima [A]  time = 1.35568, size = 103, normalized size = 1.18 \[ -\frac{2095845840 \, x^{5} + 8208729540 \, x^{4} + 13525968060 \, x^{3} + 11211272235 \, x^{2} + 4581535248 \, x + 733614062}{190591380 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac{10648}{823543} \, \log \left (3 \, x + 2\right ) - \frac{10648}{823543} \, \log \left (2 \, x - 1\right ) \]

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]

-1/190591380*(2095845840*x^5 + 8208729540*x^4 + 13525968060*x^3 + 11211272235*x^
2 + 4581535248*x + 733614062)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x
^2 + 576*x + 64) + 10648/823543*log(3*x + 2) - 10648/823543*log(2*x - 1)

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Fricas [A]  time = 0.214693, size = 182, normalized size = 2.09 \[ -\frac{14670920880 \, x^{5} + 57461106780 \, x^{4} + 94681776420 \, x^{3} + 78478905645 \, x^{2} - 17249760 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 17249760 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (2 \, x - 1\right ) + 32070746736 \, x + 5135298434}{1334139660 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]

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]

-1/1334139660*(14670920880*x^5 + 57461106780*x^4 + 94681776420*x^3 + 78478905645
*x^2 - 17249760*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 6
4)*log(3*x + 2) + 17249760*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2
+ 576*x + 64)*log(2*x - 1) + 32070746736*x + 5135298434)/(729*x^6 + 2916*x^5 + 4
860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)

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Sympy [A]  time = 0.598006, size = 75, normalized size = 0.86 \[ - \frac{2095845840 x^{5} + 8208729540 x^{4} + 13525968060 x^{3} + 11211272235 x^{2} + 4581535248 x + 733614062}{138941116020 x^{6} + 555764464080 x^{5} + 926274106800 x^{4} + 823354761600 x^{3} + 411677380800 x^{2} + 109780634880 x + 12197848320} - \frac{10648 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{10648 \log{\left (x + \frac{2}{3} \right )}}{823543} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(2095845840*x**5 + 8208729540*x**4 + 13525968060*x**3 + 11211272235*x**2 + 4581
535248*x + 733614062)/(138941116020*x**6 + 555764464080*x**5 + 926274106800*x**4
+ 823354761600*x**3 + 411677380800*x**2 + 109780634880*x + 12197848320) - 10648
*log(x - 1/2)/823543 + 10648*log(x + 2/3)/823543

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GIAC/XCAS [A]  time = 0.211924, size = 72, normalized size = 0.83 \[ -\frac{2095845840 \, x^{5} + 8208729540 \, x^{4} + 13525968060 \, x^{3} + 11211272235 \, x^{2} + 4581535248 \, x + 733614062}{190591380 \,{\left (3 \, x + 2\right )}^{6}} + \frac{10648}{823543} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{10648}{823543} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

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]

-1/190591380*(2095845840*x^5 + 8208729540*x^4 + 13525968060*x^3 + 11211272235*x^
2 + 4581535248*x + 733614062)/(3*x + 2)^6 + 10648/823543*ln(abs(3*x + 2)) - 1064
8/823543*ln(abs(2*x - 1))