3.1173 \(\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^7} \, dx\)

Optimal. Leaf size=55 \[ \frac{29 (5 x+3)^4}{36 (3 x+2)^4}+\frac{29 (5 x+3)^4}{45 (3 x+2)^5}+\frac{7 (5 x+3)^4}{18 (3 x+2)^6} \]

[Out]

(7*(3 + 5*x)^4)/(18*(2 + 3*x)^6) + (29*(3 + 5*x)^4)/(45*(2 + 3*x)^5) + (29*(3 +
5*x)^4)/(36*(2 + 3*x)^4)

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Rubi [A]  time = 0.0506789, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15 \[ \frac{29 (5 x+3)^4}{36 (3 x+2)^4}+\frac{29 (5 x+3)^4}{45 (3 x+2)^5}+\frac{7 (5 x+3)^4}{18 (3 x+2)^6} \]

Antiderivative was successfully verified.

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

[Out]

(7*(3 + 5*x)^4)/(18*(2 + 3*x)^6) + (29*(3 + 5*x)^4)/(45*(2 + 3*x)^5) + (29*(3 +
5*x)^4)/(36*(2 + 3*x)^4)

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Rubi in Sympy [A]  time = 7.00212, size = 49, normalized size = 0.89 \[ \frac{29 \left (5 x + 3\right )^{4}}{36 \left (3 x + 2\right )^{4}} + \frac{29 \left (5 x + 3\right )^{4}}{45 \left (3 x + 2\right )^{5}} + \frac{7 \left (5 x + 3\right )^{4}}{18 \left (3 x + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

29*(5*x + 3)**4/(36*(3*x + 2)**4) + 29*(5*x + 3)**4/(45*(3*x + 2)**5) + 7*(5*x +
3)**4/(18*(3*x + 2)**6)

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Mathematica [A]  time = 0.0155989, size = 31, normalized size = 0.56 \[ \frac{607500 x^4+1066500 x^3+587925 x^2+78048 x-13198}{14580 (3 x+2)^6} \]

Antiderivative was successfully verified.

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

[Out]

(-13198 + 78048*x + 587925*x^2 + 1066500*x^3 + 607500*x^4)/(14580*(2 + 3*x)^6)

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Maple [A]  time = 0.007, size = 47, normalized size = 0.9 \[ -{\frac{107}{1215\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{1025}{729\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{185}{324\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{125}{243\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{7}{1458\, \left ( 2+3\,x \right ) ^{6}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-107/1215/(2+3*x)^5-1025/729/(2+3*x)^3+185/324/(2+3*x)^4+125/243/(2+3*x)^2+7/145
8/(2+3*x)^6

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Maxima [A]  time = 1.33113, size = 73, normalized size = 1.33 \[ \frac{607500 \, x^{4} + 1066500 \, x^{3} + 587925 \, x^{2} + 78048 \, x - 13198}{14580 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/14580*(607500*x^4 + 1066500*x^3 + 587925*x^2 + 78048*x - 13198)/(729*x^6 + 291
6*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)

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Fricas [A]  time = 0.211373, size = 73, normalized size = 1.33 \[ \frac{607500 \, x^{4} + 1066500 \, x^{3} + 587925 \, x^{2} + 78048 \, x - 13198}{14580 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/14580*(607500*x^4 + 1066500*x^3 + 587925*x^2 + 78048*x - 13198)/(729*x^6 + 291
6*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)

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Sympy [A]  time = 0.430724, size = 49, normalized size = 0.89 \[ \frac{607500 x^{4} + 1066500 x^{3} + 587925 x^{2} + 78048 x - 13198}{10628820 x^{6} + 42515280 x^{5} + 70858800 x^{4} + 62985600 x^{3} + 31492800 x^{2} + 8398080 x + 933120} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(607500*x**4 + 1066500*x**3 + 587925*x**2 + 78048*x - 13198)/(10628820*x**6 + 42
515280*x**5 + 70858800*x**4 + 62985600*x**3 + 31492800*x**2 + 8398080*x + 933120
)

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GIAC/XCAS [A]  time = 0.206324, size = 39, normalized size = 0.71 \[ \frac{607500 \, x^{4} + 1066500 \, x^{3} + 587925 \, x^{2} + 78048 \, x - 13198}{14580 \,{\left (3 \, x + 2\right )}^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/14580*(607500*x^4 + 1066500*x^3 + 587925*x^2 + 78048*x - 13198)/(3*x + 2)^6