3.1174 \(\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^8} \, dx\)

Optimal. Leaf size=56 \[ \frac{250}{729 (3 x+2)^3}-\frac{1025}{972 (3 x+2)^4}+\frac{37}{81 (3 x+2)^5}-\frac{107}{1458 (3 x+2)^6}+\frac{1}{243 (3 x+2)^7} \]

[Out]

1/(243*(2 + 3*x)^7) - 107/(1458*(2 + 3*x)^6) + 37/(81*(2 + 3*x)^5) - 1025/(972*(
2 + 3*x)^4) + 250/(729*(2 + 3*x)^3)

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Rubi [A]  time = 0.0583572, antiderivative size = 56, 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 \[ \frac{250}{729 (3 x+2)^3}-\frac{1025}{972 (3 x+2)^4}+\frac{37}{81 (3 x+2)^5}-\frac{107}{1458 (3 x+2)^6}+\frac{1}{243 (3 x+2)^7} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^8,x]

[Out]

1/(243*(2 + 3*x)^7) - 107/(1458*(2 + 3*x)^6) + 37/(81*(2 + 3*x)^5) - 1025/(972*(
2 + 3*x)^4) + 250/(729*(2 + 3*x)^3)

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Rubi in Sympy [A]  time = 9.63617, size = 49, normalized size = 0.88 \[ \frac{250}{729 \left (3 x + 2\right )^{3}} - \frac{1025}{972 \left (3 x + 2\right )^{4}} + \frac{37}{81 \left (3 x + 2\right )^{5}} - \frac{107}{1458 \left (3 x + 2\right )^{6}} + \frac{1}{243 \left (3 x + 2\right )^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(3+5*x)**3/(2+3*x)**8,x)

[Out]

250/(729*(3*x + 2)**3) - 1025/(972*(3*x + 2)**4) + 37/(81*(3*x + 2)**5) - 107/(1
458*(3*x + 2)**6) + 1/(243*(3*x + 2)**7)

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Mathematica [A]  time = 0.01498, size = 31, normalized size = 0.55 \[ \frac{81000 x^4+132975 x^3+61938 x^2+642 x-3688}{2916 (3 x+2)^7} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^8,x]

[Out]

(-3688 + 642*x + 61938*x^2 + 132975*x^3 + 81000*x^4)/(2916*(2 + 3*x)^7)

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Maple [A]  time = 0.009, size = 47, normalized size = 0.8 \[{\frac{1}{243\, \left ( 2+3\,x \right ) ^{7}}}-{\frac{107}{1458\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{37}{81\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{1025}{972\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{250}{729\, \left ( 2+3\,x \right ) ^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(3+5*x)^3/(2+3*x)^8,x)

[Out]

1/243/(2+3*x)^7-107/1458/(2+3*x)^6+37/81/(2+3*x)^5-1025/972/(2+3*x)^4+250/729/(2
+3*x)^3

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Maxima [A]  time = 1.33748, size = 80, normalized size = 1.43 \[ \frac{81000 \, x^{4} + 132975 \, x^{3} + 61938 \, x^{2} + 642 \, x - 3688}{2916 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(2*x - 1)/(3*x + 2)^8,x, algorithm="maxima")

[Out]

1/2916*(81000*x^4 + 132975*x^3 + 61938*x^2 + 642*x - 3688)/(2187*x^7 + 10206*x^6
+ 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)

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Fricas [A]  time = 0.203039, size = 80, normalized size = 1.43 \[ \frac{81000 \, x^{4} + 132975 \, x^{3} + 61938 \, x^{2} + 642 \, x - 3688}{2916 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(2*x - 1)/(3*x + 2)^8,x, algorithm="fricas")

[Out]

1/2916*(81000*x^4 + 132975*x^3 + 61938*x^2 + 642*x - 3688)/(2187*x^7 + 10206*x^6
+ 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)

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Sympy [A]  time = 0.487225, size = 54, normalized size = 0.96 \[ \frac{81000 x^{4} + 132975 x^{3} + 61938 x^{2} + 642 x - 3688}{6377292 x^{7} + 29760696 x^{6} + 59521392 x^{5} + 66134880 x^{4} + 44089920 x^{3} + 17635968 x^{2} + 3919104 x + 373248} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(3+5*x)**3/(2+3*x)**8,x)

[Out]

(81000*x**4 + 132975*x**3 + 61938*x**2 + 642*x - 3688)/(6377292*x**7 + 29760696*
x**6 + 59521392*x**5 + 66134880*x**4 + 44089920*x**3 + 17635968*x**2 + 3919104*x
+ 373248)

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GIAC/XCAS [A]  time = 0.209008, size = 39, normalized size = 0.7 \[ \frac{81000 \, x^{4} + 132975 \, x^{3} + 61938 \, x^{2} + 642 \, x - 3688}{2916 \,{\left (3 \, x + 2\right )}^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(2*x - 1)/(3*x + 2)^8,x, algorithm="giac")

[Out]

1/2916*(81000*x^4 + 132975*x^3 + 61938*x^2 + 642*x - 3688)/(3*x + 2)^7