3.170 \(\int \frac{\left (b x^2+c x^4\right )^3}{x^{14}} \, dx\)

Optimal. Leaf size=39 \[ -\frac{b^3}{7 x^7}-\frac{3 b^2 c}{5 x^5}-\frac{b c^2}{x^3}-\frac{c^3}{x} \]

[Out]

-b^3/(7*x^7) - (3*b^2*c)/(5*x^5) - (b*c^2)/x^3 - c^3/x

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Rubi [A]  time = 0.0450574, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -\frac{b^3}{7 x^7}-\frac{3 b^2 c}{5 x^5}-\frac{b c^2}{x^3}-\frac{c^3}{x} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2 + c*x^4)^3/x^14,x]

[Out]

-b^3/(7*x^7) - (3*b^2*c)/(5*x^5) - (b*c^2)/x^3 - c^3/x

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Rubi in Sympy [A]  time = 9.885, size = 34, normalized size = 0.87 \[ - \frac{b^{3}}{7 x^{7}} - \frac{3 b^{2} c}{5 x^{5}} - \frac{b c^{2}}{x^{3}} - \frac{c^{3}}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((c*x**4+b*x**2)**3/x**14,x)

[Out]

-b**3/(7*x**7) - 3*b**2*c/(5*x**5) - b*c**2/x**3 - c**3/x

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Mathematica [A]  time = 0.006751, size = 39, normalized size = 1. \[ -\frac{b^3}{7 x^7}-\frac{3 b^2 c}{5 x^5}-\frac{b c^2}{x^3}-\frac{c^3}{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2 + c*x^4)^3/x^14,x]

[Out]

-b^3/(7*x^7) - (3*b^2*c)/(5*x^5) - (b*c^2)/x^3 - c^3/x

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Maple [A]  time = 0.007, size = 36, normalized size = 0.9 \[ -{\frac{{b}^{3}}{7\,{x}^{7}}}-{\frac{3\,{b}^{2}c}{5\,{x}^{5}}}-{\frac{b{c}^{2}}{{x}^{3}}}-{\frac{{c}^{3}}{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((c*x^4+b*x^2)^3/x^14,x)

[Out]

-1/7*b^3/x^7-3/5*b^2*c/x^5-b*c^2/x^3-c^3/x

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Maxima [A]  time = 0.692415, size = 50, normalized size = 1.28 \[ -\frac{35 \, c^{3} x^{6} + 35 \, b c^{2} x^{4} + 21 \, b^{2} c x^{2} + 5 \, b^{3}}{35 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)^3/x^14,x, algorithm="maxima")

[Out]

-1/35*(35*c^3*x^6 + 35*b*c^2*x^4 + 21*b^2*c*x^2 + 5*b^3)/x^7

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Fricas [A]  time = 0.246176, size = 50, normalized size = 1.28 \[ -\frac{35 \, c^{3} x^{6} + 35 \, b c^{2} x^{4} + 21 \, b^{2} c x^{2} + 5 \, b^{3}}{35 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)^3/x^14,x, algorithm="fricas")

[Out]

-1/35*(35*c^3*x^6 + 35*b*c^2*x^4 + 21*b^2*c*x^2 + 5*b^3)/x^7

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Sympy [A]  time = 1.55879, size = 39, normalized size = 1. \[ - \frac{5 b^{3} + 21 b^{2} c x^{2} + 35 b c^{2} x^{4} + 35 c^{3} x^{6}}{35 x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x**4+b*x**2)**3/x**14,x)

[Out]

-(5*b**3 + 21*b**2*c*x**2 + 35*b*c**2*x**4 + 35*c**3*x**6)/(35*x**7)

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GIAC/XCAS [A]  time = 0.267991, size = 50, normalized size = 1.28 \[ -\frac{35 \, c^{3} x^{6} + 35 \, b c^{2} x^{4} + 21 \, b^{2} c x^{2} + 5 \, b^{3}}{35 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)^3/x^14,x, algorithm="giac")

[Out]

-1/35*(35*c^3*x^6 + 35*b*c^2*x^4 + 21*b^2*c*x^2 + 5*b^3)/x^7