3.88.5 \(\int \frac {1}{2} (14+13 x) \, dx\)

Optimal. Leaf size=22 \[ 1-e^2+x+x^2+\left (2+\frac {3 x}{2}\right )^2+\log (4) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.50, 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}{52} (13 x+14)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(14 + 13*x)/2,x]

[Out]

(14 + 13*x)^2/52

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}{52} (14+13 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.50 \begin {gather*} 7 x+\frac {13 x^2}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(14 + 13*x)/2,x]

[Out]

7*x + (13*x^2)/4

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fricas [A]  time = 0.51, size = 9, normalized size = 0.41 \begin {gather*} \frac {13}{4} \, x^{2} + 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(13/2*x+7,x, algorithm="fricas")

[Out]

13/4*x^2 + 7*x

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giac [A]  time = 0.12, size = 9, normalized size = 0.41 \begin {gather*} \frac {13}{4} \, x^{2} + 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(13/2*x+7,x, algorithm="giac")

[Out]

13/4*x^2 + 7*x

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maple [A]  time = 0.01, size = 9, normalized size = 0.41

method	result	size
gosper	\(\frac {x \left (13 x +28\right )}{4}\)	\(9\)
default	\(\frac {13}{4} x^{2}+7 x\)	\(10\)
norman	\(\frac {13}{4} x^{2}+7 x\)	\(10\)
risch	\(\frac {13}{4} x^{2}+7 x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(13/2*x+7,x,method=_RETURNVERBOSE)

[Out]

1/4*x*(13*x+28)

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maxima [A]  time = 0.34, size = 9, normalized size = 0.41 \begin {gather*} \frac {13}{4} \, x^{2} + 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(13/2*x+7,x, algorithm="maxima")

[Out]

13/4*x^2 + 7*x

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mupad [B]  time = 0.03, size = 8, normalized size = 0.36 \begin {gather*} \frac {x\,\left (13\,x+28\right )}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((13*x)/2 + 7,x)

[Out]

(x*(13*x + 28))/4

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sympy [A]  time = 0.04, size = 8, normalized size = 0.36 \begin {gather*} \frac {13 x^{2}}{4} + 7 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(13/2*x+7,x)

[Out]

13*x**2/4 + 7*x

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