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

Optimal result

Integrand size = 7, antiderivative size = 11 \[ \int (-2+7 x)^3 \, dx=\frac {1}{28} (2-7 x)^4 \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32} \[ \int (-2+7 x)^3 \, dx=\frac {1}{28} (2-7 x)^4 \]

[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*} \text {integral}& = \frac {1}{28} (2-7 x)^4 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int (-2+7 x)^3 \, dx=\frac {1}{28} (-2+7 x)^4 \]

[In]

Integrate[(-2 + 7*x)^3,x]

[Out]

(-2 + 7*x)^4/28

Maple [A] (verified)

Time = 0.80 (sec) , antiderivative size = 10, normalized size of antiderivative = 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	\(\frac {343}{4} x^{4}-98 x^{3}+42 x^{2}-8 x\)	\(20\)
parallelrisch	\(\frac {343}{4} x^{4}-98 x^{3}+42 x^{2}-8 x\)	\(20\)
risch	\(\frac {343}{4} x^{4}-98 x^{3}+42 x^{2}-8 x +\frac {4}{7}\)	\(21\)

[In]

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

[Out]

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

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 19 vs. \(2 (9) = 18\).

Time = 0.23 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.73 \[ \int (-2+7 x)^3 \, dx=\frac {343}{4} \, x^{4} - 98 \, x^{3} + 42 \, x^{2} - 8 \, x \]

[In]

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

[Out]

343/4*x^4 - 98*x^3 + 42*x^2 - 8*x

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 19 vs. \(2 (7) = 14\).

Time = 0.02 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.73 \[ \int (-2+7 x)^3 \, dx=\frac {343 x^{4}}{4} - 98 x^{3} + 42 x^{2} - 8 x \]

[In]

integrate((-2+7*x)**3,x)

[Out]

343*x**4/4 - 98*x**3 + 42*x**2 - 8*x

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 19 vs. \(2 (9) = 18\).

Time = 0.18 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.73 \[ \int (-2+7 x)^3 \, dx=\frac {343}{4} \, x^{4} - 98 \, x^{3} + 42 \, x^{2} - 8 \, x \]

[In]

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

[Out]

343/4*x^4 - 98*x^3 + 42*x^2 - 8*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int (-2+7 x)^3 \, dx=\frac {1}{28} \, {\left (7 \, x - 2\right )}^{4} \]

[In]

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

[Out]

1/28*(7*x - 2)^4

Mupad [B] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int (-2+7 x)^3 \, dx=\frac {{\left (7\,x-2\right )}^4}{28} \]

[In]

int((7*x - 2)^3,x)

[Out]

(7*x - 2)^4/28