3.44.67 \(\int \frac {1}{8} (250-125 x) \, dx\)

Optimal. Leaf size=20 \[ -2+e^5+5 \left (3-\frac {25}{16} (2-x)^2\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.55, 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 {125}{16} (2-x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(250 - 125*x)/8,x]

[Out]

(-125*(2 - x)^2)/16

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 {125}{16} (2-x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 0.75 \begin {gather*} -\frac {125}{8} \left (-2 x+\frac {x^2}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(250 - 125*x)/8,x]

[Out]

(-125*(-2*x + x^2/2))/8

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fricas [A]  time = 0.70, size = 9, normalized size = 0.45 \begin {gather*} -\frac {125}{16} \, x^{2} + \frac {125}{4} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-125/8*x+125/4,x, algorithm="fricas")

[Out]

-125/16*x^2 + 125/4*x

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giac [A]  time = 0.14, size = 9, normalized size = 0.45 \begin {gather*} -\frac {125}{16} \, x^{2} + \frac {125}{4} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-125/8*x+125/4,x, algorithm="giac")

[Out]

-125/16*x^2 + 125/4*x

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maple [A]  time = 0.01, size = 7, normalized size = 0.35

method	result	size
gosper	\(-\frac {125 \left (x -4\right ) x}{16}\)	\(7\)
default	\(-\frac {125}{16} x^{2}+\frac {125}{4} x\)	\(10\)
norman	\(-\frac {125}{16} x^{2}+\frac {125}{4} x\)	\(10\)
risch	\(-\frac {125}{16} x^{2}+\frac {125}{4} x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-125/8*x+125/4,x,method=_RETURNVERBOSE)

[Out]

-125/16*(x-4)*x

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maxima [A]  time = 0.41, size = 9, normalized size = 0.45 \begin {gather*} -\frac {125}{16} \, x^{2} + \frac {125}{4} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-125/8*x+125/4,x, algorithm="maxima")

[Out]

-125/16*x^2 + 125/4*x

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mupad [B]  time = 0.03, size = 6, normalized size = 0.30 \begin {gather*} -\frac {125\,x\,\left (x-4\right )}{16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(125/4 - (125*x)/8,x)

[Out]

-(125*x*(x - 4))/16

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sympy [A]  time = 0.04, size = 10, normalized size = 0.50 \begin {gather*} - \frac {125 x^{2}}{16} + \frac {125 x}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-125/8*x+125/4,x)

[Out]

-125*x**2/16 + 125*x/4

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