3.52.10 \(\int \frac {1}{25} (92-2 x) \, dx\)

Optimal. Leaf size=21 \[ 6-e+2 x-\left (-5+\frac {4+x}{5}\right )^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.52, 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 {1}{25} (46-x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(92 - 2*x)/25,x]

[Out]

-1/25*(46 - x)^2

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 {1}{25} (46-x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 0.71 \begin {gather*} -\frac {2}{25} \left (-46 x+\frac {x^2}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(92 - 2*x)/25,x]

[Out]

(-2*(-46*x + x^2/2))/25

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fricas [A]  time = 0.55, size = 9, normalized size = 0.43 \begin {gather*} -\frac {1}{25} \, x^{2} + \frac {92}{25} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/25*x+92/25,x, algorithm="fricas")

[Out]

-1/25*x^2 + 92/25*x

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giac [A]  time = 0.14, size = 9, normalized size = 0.43 \begin {gather*} -\frac {1}{25} \, x^{2} + \frac {92}{25} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/25*x+92/25,x, algorithm="giac")

[Out]

-1/25*x^2 + 92/25*x

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maple [A]  time = 0.02, size = 7, normalized size = 0.33

method	result	size
gosper	\(-\frac {x \left (x -92\right )}{25}\)	\(7\)
default	\(-\frac {1}{25} x^{2}+\frac {92}{25} x\)	\(10\)
norman	\(-\frac {1}{25} x^{2}+\frac {92}{25} x\)	\(10\)
risch	\(-\frac {1}{25} x^{2}+\frac {92}{25} x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2/25*x+92/25,x,method=_RETURNVERBOSE)

[Out]

-1/25*x*(x-92)

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maxima [A]  time = 0.34, size = 9, normalized size = 0.43 \begin {gather*} -\frac {1}{25} \, x^{2} + \frac {92}{25} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/25*x+92/25,x, algorithm="maxima")

[Out]

-1/25*x^2 + 92/25*x

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mupad [B]  time = 0.03, size = 6, normalized size = 0.29 \begin {gather*} -\frac {x\,\left (x-92\right )}{25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(92/25 - (2*x)/25,x)

[Out]

-(x*(x - 92))/25

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sympy [A]  time = 0.04, size = 8, normalized size = 0.38 \begin {gather*} - \frac {x^{2}}{25} + \frac {92 x}{25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/25*x+92/25,x)

[Out]

-x**2/25 + 92*x/25

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