3.184 \(\int \frac{x^3}{\left (2-5 x^2\right )^7} \, dx\)

Optimal. Leaf size=27 \[ \frac{1}{150 \left (2-5 x^2\right )^6}-\frac{1}{250 \left (2-5 x^2\right )^5} \]

[Out]

1/(150*(2 - 5*x^2)^6) - 1/(250*(2 - 5*x^2)^5)

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Rubi [A]  time = 0.0410365, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{1}{150 \left (2-5 x^2\right )^6}-\frac{1}{250 \left (2-5 x^2\right )^5} \]

Antiderivative was successfully verified.

[In]  Int[x^3/(2 - 5*x^2)^7,x]

[Out]

1/(150*(2 - 5*x^2)^6) - 1/(250*(2 - 5*x^2)^5)

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Rubi in Sympy [A]  time = 3.22999, size = 22, normalized size = 0.81 \[ - \frac{1}{250 \left (- 5 x^{2} + 2\right )^{5}} + \frac{1}{150 \left (- 5 x^{2} + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/(250*(-5*x**2 + 2)**5) + 1/(150*(-5*x**2 + 2)**6)

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Mathematica [A]  time = 0.0108385, size = 20, normalized size = 0.74 \[ \frac{15 x^2-1}{750 \left (2-5 x^2\right )^6} \]

Antiderivative was successfully verified.

[In]  Integrate[x^3/(2 - 5*x^2)^7,x]

[Out]

(-1 + 15*x^2)/(750*(2 - 5*x^2)^6)

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Maple [A]  time = 0.013, size = 24, normalized size = 0.9 \[{\frac{1}{150\, \left ( 5\,{x}^{2}-2 \right ) ^{6}}}+{\frac{1}{250\, \left ( 5\,{x}^{2}-2 \right ) ^{5}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3/(-5*x^2+2)^7,x)

[Out]

1/150/(5*x^2-2)^6+1/250/(5*x^2-2)^5

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Maxima [A]  time = 1.39956, size = 58, normalized size = 2.15 \[ \frac{15 \, x^{2} - 1}{750 \,{\left (15625 \, x^{12} - 37500 \, x^{10} + 37500 \, x^{8} - 20000 \, x^{6} + 6000 \, x^{4} - 960 \, x^{2} + 64\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/750*(15*x^2 - 1)/(15625*x^12 - 37500*x^10 + 37500*x^8 - 20000*x^6 + 6000*x^4 -
960*x^2 + 64)

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Fricas [A]  time = 0.194346, size = 58, normalized size = 2.15 \[ \frac{15 \, x^{2} - 1}{750 \,{\left (15625 \, x^{12} - 37500 \, x^{10} + 37500 \, x^{8} - 20000 \, x^{6} + 6000 \, x^{4} - 960 \, x^{2} + 64\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/750*(15*x^2 - 1)/(15625*x^12 - 37500*x^10 + 37500*x^8 - 20000*x^6 + 6000*x^4 -
960*x^2 + 64)

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Sympy [A]  time = 0.279183, size = 37, normalized size = 1.37 \[ \frac{15 x^{2} - 1}{11718750 x^{12} - 28125000 x^{10} + 28125000 x^{8} - 15000000 x^{6} + 4500000 x^{4} - 720000 x^{2} + 48000} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(15*x**2 - 1)/(11718750*x**12 - 28125000*x**10 + 28125000*x**8 - 15000000*x**6 +
4500000*x**4 - 720000*x**2 + 48000)

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GIAC/XCAS [A]  time = 0.202066, size = 24, normalized size = 0.89 \[ \frac{15 \, x^{2} - 1}{750 \,{\left (5 \, x^{2} - 2\right )}^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/750*(15*x^2 - 1)/(5*x^2 - 2)^6