3.93.63 \(\int \frac {1}{3} (1-6 x) \, dx\)

Optimal. Leaf size=30 \[ 5-x^2+\frac {1}{3} \left (x+\log \left (5+e^2\right )-\log \left (\frac {e^2}{\log (2)}\right )\right ) \]

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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 {1}{36} (1-6 x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 - 6*x)/3,x]

[Out]

-1/36*(1 - 6*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}{36} (1-6 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.37 \begin {gather*} \frac {x}{3}-x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 6*x)/3,x]

[Out]

x/3 - x^2

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fricas [A]  time = 0.70, size = 9, normalized size = 0.30 \begin {gather*} -x^{2} + \frac {1}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3-2*x,x, algorithm="fricas")

[Out]

-x^2 + 1/3*x

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giac [A]  time = 0.13, size = 9, normalized size = 0.30 \begin {gather*} -x^{2} + \frac {1}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3-2*x,x, algorithm="giac")

[Out]

-x^2 + 1/3*x

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maple [A]  time = 0.01, size = 9, normalized size = 0.30

method	result	size
gosper	\(-\frac {x \left (3 x -1\right )}{3}\)	\(9\)
default	\(\frac {1}{3} x -x^{2}\)	\(10\)
norman	\(\frac {1}{3} x -x^{2}\)	\(10\)
risch	\(\frac {1}{3} x -x^{2}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/3-2*x,x,method=_RETURNVERBOSE)

[Out]

-1/3*x*(3*x-1)

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maxima [A]  time = 0.35, size = 9, normalized size = 0.30 \begin {gather*} -x^{2} + \frac {1}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3-2*x,x, algorithm="maxima")

[Out]

-x^2 + 1/3*x

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mupad [B]  time = 0.03, size = 8, normalized size = 0.27 \begin {gather*} -\frac {x\,\left (3\,x-1\right )}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/3 - 2*x,x)

[Out]

-(x*(3*x - 1))/3

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sympy [A]  time = 0.05, size = 5, normalized size = 0.17 \begin {gather*} - x^{2} + \frac {x}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3-2*x,x)

[Out]

-x**2 + x/3

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