3.5.77 \(\int (-2+7 x)^3 \, dx\) [477]

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

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {1}{28} (2-7 x)^4 \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} \frac {1}{28} (-2+7 x)^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2 + 7*x)^3,x]

[Out]

(-2 + 7*x)^4/28

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Maple [A]
time = 0.20, size = 10, normalized size = 0.91

method	result	size
default	\(\frac {\left (-2+7 x \right )^{4}}{28}\)	\(10\)
gosper	\(\frac {343}{4} x^{4}-98 x^{3}+42 x^{2}-8 x\)	\(20\)
norman	\(\frac {343}{4} x^{4}-98 x^{3}+42 x^{2}-8 x\)	\(20\)
risch	\(\frac {343}{4} x^{4}-98 x^{3}+42 x^{2}-8 x +\frac {4}{7}\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-2+7*x)^3,x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 19 vs. \(2 (9) = 18\).
time = 0.27, size = 19, normalized size = 1.73 \begin {gather*} \frac {343}{4} \, x^{4} - 98 \, x^{3} + 42 \, x^{2} - 8 \, x \end {gather*}

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] Leaf count of result is larger than twice the leaf count of optimal. 19 vs. \(2 (9) = 18\).
time = 0.37, size = 19, normalized size = 1.73 \begin {gather*} \frac {343}{4} \, x^{4} - 98 \, x^{3} + 42 \, x^{2} - 8 \, x \end {gather*}

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] Leaf count of result is larger than twice the leaf count of optimal. 19 vs. \(2 (7) = 14\).
time = 0.01, size = 19, normalized size = 1.73 \begin {gather*} \frac {343 x^{4}}{4} - 98 x^{3} + 42 x^{2} - 8 x \end {gather*}

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 = 3.95, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{28} \, {\left (7 \, x - 2\right )}^{4} \end {gather*}

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

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Mupad [B]
time = 0.14, size = 9, normalized size = 0.82 \begin {gather*} \frac {{\left (7\,x-2\right )}^4}{28} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((7*x - 2)^3,x)

[Out]

(7*x - 2)^4/28

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