3.24.34 \(\int \frac {1}{3} (-5+6 x) \, dx\)

Optimal. Leaf size=15 \[ -1-\frac {1}{e}-\frac {5 x}{3}+x^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.73, 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} (5-6 x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-5 + 6*x)/3,x]

[Out]

(5 - 6*x)^2/36

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} (5-6 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.60 \begin {gather*} -\frac {5 x}{3}+x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-5 + 6*x)/3,x]

[Out]

(-5*x)/3 + x^2

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fricas [A]  time = 0.82, size = 7, normalized size = 0.47 \begin {gather*} x^{2} - \frac {5}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x-5/3,x, algorithm="fricas")

[Out]

x^2 - 5/3*x

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giac [A]  time = 0.23, size = 7, normalized size = 0.47 \begin {gather*} x^{2} - \frac {5}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x-5/3,x, algorithm="giac")

[Out]

x^2 - 5/3*x

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maple [A]  time = 0.02, size = 8, normalized size = 0.53

method	result	size
default	\(x^{2}-\frac {5}{3} x\)	\(8\)
norman	\(x^{2}-\frac {5}{3} x\)	\(8\)
risch	\(x^{2}-\frac {5}{3} x\)	\(8\)
gosper	\(\frac {x \left (3 x -5\right )}{3}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x-5/3,x,method=_RETURNVERBOSE)

[Out]

x^2-5/3*x

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maxima [A]  time = 0.56, size = 7, normalized size = 0.47 \begin {gather*} x^{2} - \frac {5}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x-5/3,x, algorithm="maxima")

[Out]

x^2 - 5/3*x

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mupad [B]  time = 0.03, size = 8, normalized size = 0.53 \begin {gather*} \frac {x\,\left (3\,x-5\right )}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x - 5/3,x)

[Out]

(x*(3*x - 5))/3

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sympy [A]  time = 0.04, size = 7, normalized size = 0.47 \begin {gather*} x^{2} - \frac {5 x}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x-5/3,x)

[Out]

x**2 - 5*x/3

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