3.87.99 \(\int \frac {1}{50} (75+116 x) \, dx\)

Optimal. Leaf size=18 \[ 5+\frac {3 x}{2}+\frac {29 x^2}{25}-\log (2) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.61, 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 {(116 x+75)^2}{11600} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(75 + 116*x)/50,x]

[Out]

(75 + 116*x)^2/11600

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 {(75+116 x)^2}{11600}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.72 \begin {gather*} \frac {3 x}{2}+\frac {29 x^2}{25} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(75 + 116*x)/50,x]

[Out]

(3*x)/2 + (29*x^2)/25

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fricas [A]  time = 0.67, size = 9, normalized size = 0.50 \begin {gather*} \frac {29}{25} \, x^{2} + \frac {3}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(58/25*x+3/2,x, algorithm="fricas")

[Out]

29/25*x^2 + 3/2*x

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giac [A]  time = 0.12, size = 9, normalized size = 0.50 \begin {gather*} \frac {29}{25} \, x^{2} + \frac {3}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(58/25*x+3/2,x, algorithm="giac")

[Out]

29/25*x^2 + 3/2*x

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maple [A]  time = 0.02, size = 9, normalized size = 0.50

method	result	size
gosper	\(\frac {x \left (58 x +75\right )}{50}\)	\(9\)
default	\(\frac {29}{25} x^{2}+\frac {3}{2} x\)	\(10\)
norman	\(\frac {29}{25} x^{2}+\frac {3}{2} x\)	\(10\)
risch	\(\frac {29}{25} x^{2}+\frac {3}{2} x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(58/25*x+3/2,x,method=_RETURNVERBOSE)

[Out]

1/50*x*(58*x+75)

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maxima [A]  time = 0.35, size = 9, normalized size = 0.50 \begin {gather*} \frac {29}{25} \, x^{2} + \frac {3}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(58/25*x+3/2,x, algorithm="maxima")

[Out]

29/25*x^2 + 3/2*x

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mupad [B]  time = 0.03, size = 8, normalized size = 0.44 \begin {gather*} \frac {x\,\left (58\,x+75\right )}{50} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((58*x)/25 + 3/2,x)

[Out]

(x*(58*x + 75))/50

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sympy [A]  time = 0.04, size = 10, normalized size = 0.56 \begin {gather*} \frac {29 x^{2}}{25} + \frac {3 x}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(58/25*x+3/2,x)

[Out]

29*x**2/25 + 3*x/2

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