3.173 \(\int \frac{\left (b x^2+c x^4\right )^3}{x^{17}} \, dx\)

Optimal. Leaf size=40 \[ \frac{c \left (b+c x^2\right )^4}{40 b^2 x^8}-\frac{\left (b+c x^2\right )^4}{10 b x^{10}} \]

[Out]

-(b + c*x^2)^4/(10*b*x^10) + (c*(b + c*x^2)^4)/(40*b^2*x^8)

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Rubi [A]  time = 0.0604499, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.235 \[ \frac{c \left (b+c x^2\right )^4}{40 b^2 x^8}-\frac{\left (b+c x^2\right )^4}{10 b x^{10}} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2 + c*x^4)^3/x^17,x]

[Out]

-(b + c*x^2)^4/(10*b*x^10) + (c*(b + c*x^2)^4)/(40*b^2*x^8)

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Rubi in Sympy [A]  time = 11.8384, size = 39, normalized size = 0.98 \[ - \frac{b^{3}}{10 x^{10}} - \frac{3 b^{2} c}{8 x^{8}} - \frac{b c^{2}}{2 x^{6}} - \frac{c^{3}}{4 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((c*x**4+b*x**2)**3/x**17,x)

[Out]

-b**3/(10*x**10) - 3*b**2*c/(8*x**8) - b*c**2/(2*x**6) - c**3/(4*x**4)

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Mathematica [A]  time = 0.00677212, size = 43, normalized size = 1.08 \[ -\frac{b^3}{10 x^{10}}-\frac{3 b^2 c}{8 x^8}-\frac{b c^2}{2 x^6}-\frac{c^3}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2 + c*x^4)^3/x^17,x]

[Out]

-b^3/(10*x^10) - (3*b^2*c)/(8*x^8) - (b*c^2)/(2*x^6) - c^3/(4*x^4)

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Maple [A]  time = 0.008, size = 36, normalized size = 0.9 \[ -{\frac{3\,{b}^{2}c}{8\,{x}^{8}}}-{\frac{b{c}^{2}}{2\,{x}^{6}}}-{\frac{{b}^{3}}{10\,{x}^{10}}}-{\frac{{c}^{3}}{4\,{x}^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((c*x^4+b*x^2)^3/x^17,x)

[Out]

-3/8*b^2*c/x^8-1/2*b*c^2/x^6-1/10*b^3/x^10-1/4*c^3/x^4

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Maxima [A]  time = 0.68679, size = 50, normalized size = 1.25 \[ -\frac{10 \, c^{3} x^{6} + 20 \, b c^{2} x^{4} + 15 \, b^{2} c x^{2} + 4 \, b^{3}}{40 \, x^{10}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)^3/x^17,x, algorithm="maxima")

[Out]

-1/40*(10*c^3*x^6 + 20*b*c^2*x^4 + 15*b^2*c*x^2 + 4*b^3)/x^10

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Fricas [A]  time = 0.245115, size = 50, normalized size = 1.25 \[ -\frac{10 \, c^{3} x^{6} + 20 \, b c^{2} x^{4} + 15 \, b^{2} c x^{2} + 4 \, b^{3}}{40 \, x^{10}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)^3/x^17,x, algorithm="fricas")

[Out]

-1/40*(10*c^3*x^6 + 20*b*c^2*x^4 + 15*b^2*c*x^2 + 4*b^3)/x^10

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Sympy [A]  time = 1.71445, size = 39, normalized size = 0.98 \[ - \frac{4 b^{3} + 15 b^{2} c x^{2} + 20 b c^{2} x^{4} + 10 c^{3} x^{6}}{40 x^{10}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x**4+b*x**2)**3/x**17,x)

[Out]

-(4*b**3 + 15*b**2*c*x**2 + 20*b*c**2*x**4 + 10*c**3*x**6)/(40*x**10)

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GIAC/XCAS [A]  time = 0.2689, size = 50, normalized size = 1.25 \[ -\frac{10 \, c^{3} x^{6} + 20 \, b c^{2} x^{4} + 15 \, b^{2} c x^{2} + 4 \, b^{3}}{40 \, x^{10}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)^3/x^17,x, algorithm="giac")

[Out]

-1/40*(10*c^3*x^6 + 20*b*c^2*x^4 + 15*b^2*c*x^2 + 4*b^3)/x^10