3.29.66 \(\int \frac {1}{3} (-8+18 x) \, dx\)

Optimal. Leaf size=16 \[ -5+x^2+x \left (-\frac {8}{3}+2 x\right )+\log (3) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.69, 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}{27} (4-9 x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-8 + 18*x)/3,x]

[Out]

(4 - 9*x)^2/27

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}{27} (4-9 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.69 \begin {gather*} -\frac {8 x}{3}+3 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-8 + 18*x)/3,x]

[Out]

(-8*x)/3 + 3*x^2

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fricas [A]  time = 0.47, size = 9, normalized size = 0.56 \begin {gather*} 3 \, x^{2} - \frac {8}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x-8/3,x, algorithm="fricas")

[Out]

3*x^2 - 8/3*x

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giac [A]  time = 0.22, size = 9, normalized size = 0.56 \begin {gather*} 3 \, x^{2} - \frac {8}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x-8/3,x, algorithm="giac")

[Out]

3*x^2 - 8/3*x

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maple [A]  time = 0.01, size = 9, normalized size = 0.56

method	result	size
gosper	\(\frac {x \left (9 x -8\right )}{3}\)	\(9\)
default	\(3 x^{2}-\frac {8}{3} x\)	\(10\)
norman	\(3 x^{2}-\frac {8}{3} x\)	\(10\)
risch	\(3 x^{2}-\frac {8}{3} x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*x-8/3,x,method=_RETURNVERBOSE)

[Out]

1/3*x*(9*x-8)

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maxima [A]  time = 0.43, size = 9, normalized size = 0.56 \begin {gather*} 3 \, x^{2} - \frac {8}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x-8/3,x, algorithm="maxima")

[Out]

3*x^2 - 8/3*x

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mupad [B]  time = 0.03, size = 8, normalized size = 0.50 \begin {gather*} \frac {x\,\left (9\,x-8\right )}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*x - 8/3,x)

[Out]

(x*(9*x - 8))/3

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sympy [A]  time = 0.04, size = 8, normalized size = 0.50 \begin {gather*} 3 x^{2} - \frac {8 x}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x-8/3,x)

[Out]

3*x**2 - 8*x/3

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