3.103.28 \(\int \frac {1}{3} (1+80 x) \, dx\)

Optimal. Leaf size=21 \[ 1+x+\frac {2}{3} \left (1-x+20 x^2-\log (2)\right ) \]

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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}{480} (80 x+1)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 + 80*x)/3,x]

[Out]

(1 + 80*x)^2/480

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}{480} (1+80 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.52 \begin {gather*} \frac {1}{3} \left (x+40 x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 + 80*x)/3,x]

[Out]

(x + 40*x^2)/3

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fricas [A]  time = 0.62, size = 9, normalized size = 0.43 \begin {gather*} \frac {40}{3} \, x^{2} + \frac {1}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(80/3*x+1/3,x, algorithm="fricas")

[Out]

40/3*x^2 + 1/3*x

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giac [A]  time = 0.18, size = 9, normalized size = 0.43 \begin {gather*} \frac {40}{3} \, x^{2} + \frac {1}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(80/3*x+1/3,x, algorithm="giac")

[Out]

40/3*x^2 + 1/3*x

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maple [A]  time = 0.01, size = 9, normalized size = 0.43

method	result	size
gosper	\(\frac {x \left (40 x +1\right )}{3}\)	\(9\)
default	\(\frac {40}{3} x^{2}+\frac {1}{3} x\)	\(10\)
norman	\(\frac {40}{3} x^{2}+\frac {1}{3} x\)	\(10\)
risch	\(\frac {40}{3} x^{2}+\frac {1}{3} x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(80/3*x+1/3,x,method=_RETURNVERBOSE)

[Out]

1/3*x*(40*x+1)

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maxima [A]  time = 0.36, size = 9, normalized size = 0.43 \begin {gather*} \frac {40}{3} \, x^{2} + \frac {1}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(80/3*x+1/3,x, algorithm="maxima")

[Out]

40/3*x^2 + 1/3*x

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mupad [B]  time = 0.04, size = 8, normalized size = 0.38 \begin {gather*} \frac {x\,\left (40\,x+1\right )}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((80*x)/3 + 1/3,x)

[Out]

(x*(40*x + 1))/3

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sympy [A]  time = 0.05, size = 8, normalized size = 0.38 \begin {gather*} \frac {40 x^{2}}{3} + \frac {x}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(80/3*x+1/3,x)

[Out]

40*x**2/3 + x/3

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