3.62.80 \(\int \frac {1}{16} (1-31 x) \, dx\)

Optimal. Leaf size=21 \[ \sqrt [16]{e}+x \left (-x+\frac {1}{64} (4+2 x)\right ) \]

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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}{992} (1-31 x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 31*x)/16,x]

[Out]

-1/992*(1 - 31*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}{992} (1-31 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.62 \begin {gather*} \frac {1}{16} \left (x-\frac {31 x^2}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 31*x)/16,x]

[Out]

(x - (31*x^2)/2)/16

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fricas [A]  time = 0.60, size = 9, normalized size = 0.43 \begin {gather*} -\frac {31}{32} \, x^{2} + \frac {1}{16} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-31/16*x+1/16,x, algorithm="fricas")

[Out]

-31/32*x^2 + 1/16*x

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giac [A]  time = 0.23, size = 9, normalized size = 0.43 \begin {gather*} -\frac {31}{32} \, x^{2} + \frac {1}{16} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-31/16*x+1/16,x, algorithm="giac")

[Out]

-31/32*x^2 + 1/16*x

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maple [A]  time = 0.02, size = 9, normalized size = 0.43

method	result	size
gosper	\(-\frac {x \left (31 x -2\right )}{32}\)	\(9\)
default	\(-\frac {31}{32} x^{2}+\frac {1}{16} x\)	\(10\)
norman	\(-\frac {31}{32} x^{2}+\frac {1}{16} x\)	\(10\)
risch	\(-\frac {31}{32} x^{2}+\frac {1}{16} x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-31/16*x+1/16,x,method=_RETURNVERBOSE)

[Out]

-1/32*x*(31*x-2)

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maxima [A]  time = 0.35, size = 9, normalized size = 0.43 \begin {gather*} -\frac {31}{32} \, x^{2} + \frac {1}{16} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-31/16*x+1/16,x, algorithm="maxima")

[Out]

-31/32*x^2 + 1/16*x

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mupad [B]  time = 0.03, size = 8, normalized size = 0.38 \begin {gather*} -\frac {x\,\left (31\,x-2\right )}{32} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/16 - (31*x)/16,x)

[Out]

-(x*(31*x - 2))/32

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sympy [A]  time = 0.04, size = 8, normalized size = 0.38 \begin {gather*} - \frac {31 x^{2}}{32} + \frac {x}{16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-31/16*x+1/16,x)

[Out]

-31*x**2/32 + x/16

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