3.171 \(\int \frac{\left (b x^2+c x^4\right )^3}{x^{15}} \, dx\)

Optimal. Leaf size=19 \[ -\frac{\left (b+c x^2\right )^4}{8 b x^8} \]

[Out]

-(b + c*x^2)^4/(8*b*x^8)

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Rubi [A]  time = 0.0228797, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -\frac{\left (b+c x^2\right )^4}{8 b x^8} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2 + c*x^4)^3/x^15,x]

[Out]

-(b + c*x^2)^4/(8*b*x^8)

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Rubi in Sympy [A]  time = 5.16102, size = 15, normalized size = 0.79 \[ - \frac{\left (b + c x^{2}\right )^{4}}{8 b x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((c*x**4+b*x**2)**3/x**15,x)

[Out]

-(b + c*x**2)**4/(8*b*x**8)

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Mathematica [B]  time = 0.0113402, size = 43, normalized size = 2.26 \[ -\frac{b^3}{8 x^8}-\frac{b^2 c}{2 x^6}-\frac{3 b c^2}{4 x^4}-\frac{c^3}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2 + c*x^4)^3/x^15,x]

[Out]

-b^3/(8*x^8) - (b^2*c)/(2*x^6) - (3*b*c^2)/(4*x^4) - c^3/(2*x^2)

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Maple [B]  time = 0.007, size = 36, normalized size = 1.9 \[ -{\frac{{b}^{3}}{8\,{x}^{8}}}-{\frac{{b}^{2}c}{2\,{x}^{6}}}-{\frac{{c}^{3}}{2\,{x}^{2}}}-{\frac{3\,b{c}^{2}}{4\,{x}^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((c*x^4+b*x^2)^3/x^15,x)

[Out]

-1/8*b^3/x^8-1/2*b^2*c/x^6-1/2*c^3/x^2-3/4*b*c^2/x^4

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Maxima [A]  time = 0.695561, size = 47, normalized size = 2.47 \[ -\frac{4 \, c^{3} x^{6} + 6 \, b c^{2} x^{4} + 4 \, b^{2} c x^{2} + b^{3}}{8 \, x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)^3/x^15,x, algorithm="maxima")

[Out]

-1/8*(4*c^3*x^6 + 6*b*c^2*x^4 + 4*b^2*c*x^2 + b^3)/x^8

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Fricas [A]  time = 0.246106, size = 47, normalized size = 2.47 \[ -\frac{4 \, c^{3} x^{6} + 6 \, b c^{2} x^{4} + 4 \, b^{2} c x^{2} + b^{3}}{8 \, x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)^3/x^15,x, algorithm="fricas")

[Out]

-1/8*(4*c^3*x^6 + 6*b*c^2*x^4 + 4*b^2*c*x^2 + b^3)/x^8

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Sympy [A]  time = 1.63611, size = 37, normalized size = 1.95 \[ - \frac{b^{3} + 4 b^{2} c x^{2} + 6 b c^{2} x^{4} + 4 c^{3} x^{6}}{8 x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x**4+b*x**2)**3/x**15,x)

[Out]

-(b**3 + 4*b**2*c*x**2 + 6*b*c**2*x**4 + 4*c**3*x**6)/(8*x**8)

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GIAC/XCAS [A]  time = 0.268212, size = 47, normalized size = 2.47 \[ -\frac{4 \, c^{3} x^{6} + 6 \, b c^{2} x^{4} + 4 \, b^{2} c x^{2} + b^{3}}{8 \, x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)^3/x^15,x, algorithm="giac")

[Out]

-1/8*(4*c^3*x^6 + 6*b*c^2*x^4 + 4*b^2*c*x^2 + b^3)/x^8