3.477 \(\int (-2+7 x)^3 \, dx\)

Optimal. Leaf size=11 \[ \frac{1}{28} (2-7 x)^4 \]

[Out]

(2 - 7*x)^4/28

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Rubi [A]  time = 0.00656477, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{1}{28} (2-7 x)^4 \]

Antiderivative was successfully verified.

[In]  Int[(-2 + 7*x)^3,x]

[Out]

(2 - 7*x)^4/28

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Rubi in Sympy [A]  time = 1.05605, size = 7, normalized size = 0.64 \[ \frac{\left (- 7 x + 2\right )^{4}}{28} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((-2+7*x)**3,x)

[Out]

(-7*x + 2)**4/28

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Mathematica [A]  time = 0.00230804, size = 11, normalized size = 1. \[ \frac{1}{28} (7 x-2)^4 \]

Antiderivative was successfully verified.

[In]  Integrate[(-2 + 7*x)^3,x]

[Out]

(-2 + 7*x)^4/28

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Maple [A]  time = 0.001, size = 10, normalized size = 0.9 \[{\frac{ \left ( -2+7\,x \right ) ^{4}}{28}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-2+7*x)^3,x)

[Out]

1/28*(-2+7*x)^4

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Maxima [A]  time = 0.777655, size = 26, normalized size = 2.36 \[ \frac{343}{4} \, x^{4} - 98 \, x^{3} + 42 \, x^{2} - 8 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343/4*x^4 - 98*x^3 + 42*x^2 - 8*x

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Fricas [A]  time = 0.224479, size = 1, normalized size = 0.09 \[ \frac{343}{4} x^{4} - 98 x^{3} + 42 x^{2} - 8 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343/4*x^4 - 98*x^3 + 42*x^2 - 8*x

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Sympy [A]  time = 0.065656, size = 19, normalized size = 1.73 \[ \frac{343 x^{4}}{4} - 98 x^{3} + 42 x^{2} - 8 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((-2+7*x)**3,x)

[Out]

343*x**4/4 - 98*x**3 + 42*x**2 - 8*x

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GIAC/XCAS [A]  time = 0.258236, size = 12, normalized size = 1.09 \[ \frac{1}{28} \,{\left (7 \, x - 2\right )}^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/28*(7*x - 2)^4