3.1432 \(\int \frac{3+5 x}{(1-2 x) (2+3 x)^7} \, dx\)

Optimal. Leaf size=87 \[ -\frac{176}{117649 (3 x+2)}-\frac{44}{16807 (3 x+2)^2}-\frac{44}{7203 (3 x+2)^3}-\frac{11}{686 (3 x+2)^4}-\frac{11}{245 (3 x+2)^5}+\frac{1}{126 (3 x+2)^6}-\frac{352 \log (1-2 x)}{823543}+\frac{352 \log (3 x+2)}{823543} \]

[Out]

1/(126*(2 + 3*x)^6) - 11/(245*(2 + 3*x)^5) - 11/(686*(2 + 3*x)^4) - 44/(7203*(2
+ 3*x)^3) - 44/(16807*(2 + 3*x)^2) - 176/(117649*(2 + 3*x)) - (352*Log[1 - 2*x])
/823543 + (352*Log[2 + 3*x])/823543

_______________________________________________________________________________________

Rubi [A]  time = 0.0778605, antiderivative size = 87, 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 \[ -\frac{176}{117649 (3 x+2)}-\frac{44}{16807 (3 x+2)^2}-\frac{44}{7203 (3 x+2)^3}-\frac{11}{686 (3 x+2)^4}-\frac{11}{245 (3 x+2)^5}+\frac{1}{126 (3 x+2)^6}-\frac{352 \log (1-2 x)}{823543}+\frac{352 \log (3 x+2)}{823543} \]

Antiderivative was successfully verified.

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

[Out]

1/(126*(2 + 3*x)^6) - 11/(245*(2 + 3*x)^5) - 11/(686*(2 + 3*x)^4) - 44/(7203*(2
+ 3*x)^3) - 44/(16807*(2 + 3*x)^2) - 176/(117649*(2 + 3*x)) - (352*Log[1 - 2*x])
/823543 + (352*Log[2 + 3*x])/823543

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 12.0908, size = 76, normalized size = 0.87 \[ - \frac{352 \log{\left (- 2 x + 1 \right )}}{823543} + \frac{352 \log{\left (3 x + 2 \right )}}{823543} - \frac{176}{117649 \left (3 x + 2\right )} - \frac{44}{16807 \left (3 x + 2\right )^{2}} - \frac{44}{7203 \left (3 x + 2\right )^{3}} - \frac{11}{686 \left (3 x + 2\right )^{4}} - \frac{11}{245 \left (3 x + 2\right )^{5}} + \frac{1}{126 \left (3 x + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-352*log(-2*x + 1)/823543 + 352*log(3*x + 2)/823543 - 176/(117649*(3*x + 2)) - 4
4/(16807*(3*x + 2)**2) - 44/(7203*(3*x + 2)**3) - 11/(686*(3*x + 2)**4) - 11/(24
5*(3*x + 2)**5) + 1/(126*(3*x + 2)**6)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0620601, size = 55, normalized size = 0.63 \[ \frac{-\frac{7 \left (3849120 x^5+15075720 x^4+24841080 x^3+22413105 x^2+12254814 x+3013741\right )}{(3 x+2)^6}-31680 \log (3-6 x)+31680 \log (3 x+2)}{74118870} \]

Antiderivative was successfully verified.

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

[Out]

((-7*(3013741 + 12254814*x + 22413105*x^2 + 24841080*x^3 + 15075720*x^4 + 384912
0*x^5))/(2 + 3*x)^6 - 31680*Log[3 - 6*x] + 31680*Log[2 + 3*x])/74118870

_______________________________________________________________________________________

Maple [A]  time = 0.013, size = 72, normalized size = 0.8 \[{\frac{1}{126\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{11}{245\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{11}{686\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{44}{7203\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{44}{16807\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{176}{235298+352947\,x}}+{\frac{352\,\ln \left ( 2+3\,x \right ) }{823543}}-{\frac{352\,\ln \left ( -1+2\,x \right ) }{823543}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/126/(2+3*x)^6-11/245/(2+3*x)^5-11/686/(2+3*x)^4-44/7203/(2+3*x)^3-44/16807/(2+
3*x)^2-176/117649/(2+3*x)+352/823543*ln(2+3*x)-352/823543*ln(-1+2*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.3482, size = 103, normalized size = 1.18 \[ -\frac{3849120 \, x^{5} + 15075720 \, x^{4} + 24841080 \, x^{3} + 22413105 \, x^{2} + 12254814 \, x + 3013741}{10588410 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac{352}{823543} \, \log \left (3 \, x + 2\right ) - \frac{352}{823543} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/10588410*(3849120*x^5 + 15075720*x^4 + 24841080*x^3 + 22413105*x^2 + 12254814
*x + 3013741)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)
+ 352/823543*log(3*x + 2) - 352/823543*log(2*x - 1)

_______________________________________________________________________________________

Fricas [A]  time = 0.226731, size = 182, normalized size = 2.09 \[ -\frac{26943840 \, x^{5} + 105530040 \, x^{4} + 173887560 \, x^{3} + 156891735 \, x^{2} - 31680 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 31680 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (2 \, x - 1\right ) + 85783698 \, x + 21096187}{74118870 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/74118870*(26943840*x^5 + 105530040*x^4 + 173887560*x^3 + 156891735*x^2 - 3168
0*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(3*x + 2
) + 31680*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log
(2*x - 1) + 85783698*x + 21096187)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2
160*x^2 + 576*x + 64)

_______________________________________________________________________________________

Sympy [A]  time = 0.544346, size = 75, normalized size = 0.86 \[ - \frac{3849120 x^{5} + 15075720 x^{4} + 24841080 x^{3} + 22413105 x^{2} + 12254814 x + 3013741}{7718950890 x^{6} + 30875803560 x^{5} + 51459672600 x^{4} + 45741931200 x^{3} + 22870965600 x^{2} + 6098924160 x + 677658240} - \frac{352 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{352 \log{\left (x + \frac{2}{3} \right )}}{823543} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(3849120*x**5 + 15075720*x**4 + 24841080*x**3 + 22413105*x**2 + 12254814*x + 30
13741)/(7718950890*x**6 + 30875803560*x**5 + 51459672600*x**4 + 45741931200*x**3
+ 22870965600*x**2 + 6098924160*x + 677658240) - 352*log(x - 1/2)/823543 + 352*
log(x + 2/3)/823543

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.210993, size = 72, normalized size = 0.83 \[ -\frac{3849120 \, x^{5} + 15075720 \, x^{4} + 24841080 \, x^{3} + 22413105 \, x^{2} + 12254814 \, x + 3013741}{10588410 \,{\left (3 \, x + 2\right )}^{6}} + \frac{352}{823543} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{352}{823543} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/10588410*(3849120*x^5 + 15075720*x^4 + 24841080*x^3 + 22413105*x^2 + 12254814
*x + 3013741)/(3*x + 2)^6 + 352/823543*ln(abs(3*x + 2)) - 352/823543*ln(abs(2*x
- 1))