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 = 0.0010748, 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, Rules used = {32} \[ \frac{1}{28} (2-7 x)^4 \]

Antiderivative was successfully verified.

[In]

Int[(-2 + 7*x)^3,x]

[Out]

(2 - 7*x)^4/28

Rule 32

Int[((a_.) + (b_.)*(x_))^(m_), x_Symbol] :> Simp[(a + b*x)^(m + 1)/(b*(m + 1)), x] /; FreeQ[{a, b, m}, x] && N
eQ[m, -1]

Rubi steps

\begin{align*} \int (-2+7 x)^3 \, dx &=\frac{1}{28} (2-7 x)^4\\ \end{align*}

Mathematica [A]  time = 0.0014178, 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 = 0.002, size = 10, normalized size = 0.9 \begin{align*}{\frac{ \left ( -2+7\,x \right ) ^{4}}{28}} \end{align*}

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 [B]  time = 1.10926, size = 26, normalized size = 2.36 \begin{align*} \frac{343}{4} \, x^{4} - 98 \, x^{3} + 42 \, x^{2} - 8 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2+7*x)^3,x, algorithm="maxima")

[Out]

343/4*x^4 - 98*x^3 + 42*x^2 - 8*x

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Fricas [B]  time = 1.06116, size = 47, normalized size = 4.27 \begin{align*} \frac{343}{4} x^{4} - 98 x^{3} + 42 x^{2} - 8 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2+7*x)^3,x, algorithm="fricas")

[Out]

343/4*x^4 - 98*x^3 + 42*x^2 - 8*x

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Sympy [B]  time = 0.052643, size = 19, normalized size = 1.73 \begin{align*} \frac{343 x^{4}}{4} - 98 x^{3} + 42 x^{2} - 8 x \end{align*}

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 [A]  time = 1.10219, size = 12, normalized size = 1.09 \begin{align*} \frac{1}{28} \,{\left (7 \, x - 2\right )}^{4} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2+7*x)^3,x, algorithm="giac")

[Out]

1/28*(7*x - 2)^4