3.35.24 \(\int \frac {1}{5} (-738-360 x) \, dx\)

Optimal. Leaf size=21 \[ e^4+\frac {2 x}{5}-4 \left (1+x+(6+3 x)^2\right ) \]

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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 {9}{100} (20 x+41)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-738 - 360*x)/5,x]

[Out]

(-9*(41 + 20*x)^2)/100

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 {9}{100} (41+20 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.52 \begin {gather*} -\frac {738 x}{5}-36 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-738 - 360*x)/5,x]

[Out]

(-738*x)/5 - 36*x^2

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fricas [A]  time = 0.50, size = 9, normalized size = 0.43 \begin {gather*} -36 \, x^{2} - \frac {738}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-72*x-738/5,x, algorithm="fricas")

[Out]

-36*x^2 - 738/5*x

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giac [A]  time = 0.14, size = 9, normalized size = 0.43 \begin {gather*} -36 \, x^{2} - \frac {738}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-72*x-738/5,x, algorithm="giac")

[Out]

-36*x^2 - 738/5*x

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

method	result	size
gosper	\(-\frac {18 x \left (10 x +41\right )}{5}\)	\(9\)
default	\(-36 x^{2}-\frac {738}{5} x\)	\(10\)
norman	\(-36 x^{2}-\frac {738}{5} x\)	\(10\)
risch	\(-36 x^{2}-\frac {738}{5} x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-72*x-738/5,x,method=_RETURNVERBOSE)

[Out]

-18/5*x*(10*x+41)

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maxima [A]  time = 0.51, size = 9, normalized size = 0.43 \begin {gather*} -36 \, x^{2} - \frac {738}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-72*x-738/5,x, algorithm="maxima")

[Out]

-36*x^2 - 738/5*x

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mupad [B]  time = 0.03, size = 8, normalized size = 0.38 \begin {gather*} -\frac {18\,x\,\left (10\,x+41\right )}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 72*x - 738/5,x)

[Out]

-(18*x*(10*x + 41))/5

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sympy [A]  time = 0.04, size = 10, normalized size = 0.48 \begin {gather*} - 36 x^{2} - \frac {738 x}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-72*x-738/5,x)

[Out]

-36*x**2 - 738*x/5

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