3.32.22 \(\int \frac {1}{5} (-14+14 x) \, dx\)

Optimal. Leaf size=30 \[ -e^{e^5}+x+x \left (2-\frac {x+7 (4-x) x}{5 x}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.37, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {9} \begin {gather*} \frac {7}{5} (1-x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-14 + 14*x)/5,x]

[Out]

(7*(1 - x)^2)/5

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[(a*(b + c*x)^2)/(2*c), x] /; FreeQ[{a, b, c}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {7}{5} (1-x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 0.50 \begin {gather*} \frac {14}{5} \left (-x+\frac {x^2}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-14 + 14*x)/5,x]

[Out]

(14*(-x + x^2/2))/5

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fricas [A]  time = 0.56, size = 9, normalized size = 0.30 \begin {gather*} \frac {7}{5} \, x^{2} - \frac {14}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(14/5*x-14/5,x, algorithm="fricas")

[Out]

7/5*x^2 - 14/5*x

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giac [A]  time = 0.18, size = 9, normalized size = 0.30 \begin {gather*} \frac {7}{5} \, x^{2} - \frac {14}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(14/5*x-14/5,x, algorithm="giac")

[Out]

7/5*x^2 - 14/5*x

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maple [A]  time = 0.02, size = 7, normalized size = 0.23

method	result	size
gosper	\(\frac {7 \left (x -2\right ) x}{5}\)	\(7\)
default	\(\frac {7}{5} x^{2}-\frac {14}{5} x\)	\(10\)
norman	\(\frac {7}{5} x^{2}-\frac {14}{5} x\)	\(10\)
risch	\(\frac {7}{5} x^{2}-\frac {14}{5} x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(14/5*x-14/5,x,method=_RETURNVERBOSE)

[Out]

7/5*(x-2)*x

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maxima [A]  time = 0.41, size = 9, normalized size = 0.30 \begin {gather*} \frac {7}{5} \, x^{2} - \frac {14}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(14/5*x-14/5,x, algorithm="maxima")

[Out]

7/5*x^2 - 14/5*x

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mupad [B]  time = 0.03, size = 6, normalized size = 0.20 \begin {gather*} \frac {7\,x\,\left (x-2\right )}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((14*x)/5 - 14/5,x)

[Out]

(7*x*(x - 2))/5

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sympy [A]  time = 0.04, size = 10, normalized size = 0.33 \begin {gather*} \frac {7 x^{2}}{5} - \frac {14 x}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(14/5*x-14/5,x)

[Out]

7*x**2/5 - 14*x/5

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