3.476 \(\int (-3+x) \left (-7+4 x^2\right ) \, dx\)

Optimal. Leaf size=22 \[ -4 x^3+\frac{1}{16} \left (7-4 x^2\right )^2+21 x \]

[Out]

21*x - 4*x^3 + (7 - 4*x^2)^2/16

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Rubi [A]  time = 0.0181222, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -4 x^3+\frac{1}{16} \left (7-4 x^2\right )^2+21 x \]

Antiderivative was successfully verified.

[In]  Int[(-3 + x)*(-7 + 4*x^2),x]

[Out]

21*x - 4*x^3 + (7 - 4*x^2)^2/16

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ x^{4} - 4 x^{3} + 21 x - 7 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((-3+x)*(4*x**2-7),x)

[Out]

x**4 - 4*x**3 + 21*x - 7*Integral(x, x)

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Mathematica [A]  time = 0.00169975, size = 19, normalized size = 0.86 \[ x^4-4 x^3-\frac{7 x^2}{2}+21 x \]

Antiderivative was successfully verified.

[In]  Integrate[(-3 + x)*(-7 + 4*x^2),x]

[Out]

21*x - (7*x^2)/2 - 4*x^3 + x^4

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Maple [A]  time = 0.001, size = 18, normalized size = 0.8 \[{x}^{4}-4\,{x}^{3}-{\frac{7\,{x}^{2}}{2}}+21\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-3+x)*(4*x^2-7),x)

[Out]

x^4-4*x^3-7/2*x^2+21*x

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Maxima [A]  time = 0.781584, size = 23, normalized size = 1.05 \[ x^{4} - 4 \, x^{3} - \frac{7}{2} \, x^{2} + 21 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((4*x^2 - 7)*(x - 3),x, algorithm="maxima")

[Out]

x^4 - 4*x^3 - 7/2*x^2 + 21*x

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Fricas [A]  time = 0.246489, size = 1, normalized size = 0.05 \[ x^{4} - 4 x^{3} - \frac{7}{2} x^{2} + 21 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((4*x^2 - 7)*(x - 3),x, algorithm="fricas")

[Out]

x^4 - 4*x^3 - 7/2*x^2 + 21*x

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Sympy [A]  time = 0.058897, size = 17, normalized size = 0.77 \[ x^{4} - 4 x^{3} - \frac{7 x^{2}}{2} + 21 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((-3+x)*(4*x**2-7),x)

[Out]

x**4 - 4*x**3 - 7*x**2/2 + 21*x

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GIAC/XCAS [A]  time = 0.261148, size = 23, normalized size = 1.05 \[ x^{4} - 4 \, x^{3} - \frac{7}{2} \, x^{2} + 21 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((4*x^2 - 7)*(x - 3),x, algorithm="giac")

[Out]

x^4 - 4*x^3 - 7/2*x^2 + 21*x