3.145 \(\int \left (b x^2+c x^4\right )^2 \, dx\)

Optimal. Leaf size=30 \[ \frac{b^2 x^5}{5}+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9} \]

[Out]

(b^2*x^5)/5 + (2*b*c*x^7)/7 + (c^2*x^9)/9

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Rubi [A]  time = 0.0350977, antiderivative size = 30, 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 \[ \frac{b^2 x^5}{5}+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2 + c*x^4)^2,x]

[Out]

(b^2*x^5)/5 + (2*b*c*x^7)/7 + (c^2*x^9)/9

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Rubi in Sympy [A]  time = 10.835, size = 26, normalized size = 0.87 \[ \frac{b^{2} x^{5}}{5} + \frac{2 b c x^{7}}{7} + \frac{c^{2} x^{9}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b**2*x**5/5 + 2*b*c*x**7/7 + c**2*x**9/9

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Mathematica [A]  time = 0.00288497, size = 30, normalized size = 1. \[ \frac{b^2 x^5}{5}+\frac{2}{7} b c x^7+\frac{c^2 x^9}{9} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2 + c*x^4)^2,x]

[Out]

(b^2*x^5)/5 + (2*b*c*x^7)/7 + (c^2*x^9)/9

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Maple [A]  time = 0.001, size = 25, normalized size = 0.8 \[{\frac{{b}^{2}{x}^{5}}{5}}+{\frac{2\,bc{x}^{7}}{7}}+{\frac{{c}^{2}{x}^{9}}{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((c*x^4+b*x^2)^2,x)

[Out]

1/5*b^2*x^5+2/7*b*c*x^7+1/9*c^2*x^9

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Maxima [A]  time = 0.685842, size = 32, normalized size = 1.07 \[ \frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, b^{2} x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*c^2*x^9 + 2/7*b*c*x^7 + 1/5*b^2*x^5

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Fricas [A]  time = 0.232586, size = 1, normalized size = 0.03 \[ \frac{1}{9} x^{9} c^{2} + \frac{2}{7} x^{7} c b + \frac{1}{5} x^{5} b^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*x^9*c^2 + 2/7*x^7*c*b + 1/5*x^5*b^2

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Sympy [A]  time = 0.089564, size = 26, normalized size = 0.87 \[ \frac{b^{2} x^{5}}{5} + \frac{2 b c x^{7}}{7} + \frac{c^{2} x^{9}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x**4+b*x**2)**2,x)

[Out]

b**2*x**5/5 + 2*b*c*x**7/7 + c**2*x**9/9

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GIAC/XCAS [A]  time = 0.266483, size = 32, normalized size = 1.07 \[ \frac{1}{9} \, c^{2} x^{9} + \frac{2}{7} \, b c x^{7} + \frac{1}{5} \, b^{2} x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*c^2*x^9 + 2/7*b*c*x^7 + 1/5*b^2*x^5