3.64.99 \(\int (-47+32 x) \, dx\)

Optimal. Leaf size=20 \[ -e^2+x+4 (3 (1-x)+x)^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.45, number of steps used = 1, number of rules used = 0, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 16 x^2-47 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-47 + 32*x,x]

[Out]

-47*x + 16*x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-47 x+16 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.45 \begin {gather*} -47 x+16 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-47 + 32*x,x]

[Out]

-47*x + 16*x^2

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fricas [A]  time = 0.68, size = 9, normalized size = 0.45 \begin {gather*} 16 \, x^{2} - 47 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(32*x-47,x, algorithm="fricas")

[Out]

16*x^2 - 47*x

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giac [A]  time = 0.16, size = 9, normalized size = 0.45 \begin {gather*} 16 \, x^{2} - 47 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(32*x-47,x, algorithm="giac")

[Out]

16*x^2 - 47*x

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maple [A]  time = 0.02, size = 10, normalized size = 0.50

method	result	size
gosper	\(16 x^{2}-47 x\)	\(10\)
default	\(16 x^{2}-47 x\)	\(10\)
norman	\(16 x^{2}-47 x\)	\(10\)
risch	\(16 x^{2}-47 x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32*x-47,x,method=_RETURNVERBOSE)

[Out]

16*x^2-47*x

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maxima [A]  time = 0.37, size = 9, normalized size = 0.45 \begin {gather*} 16 \, x^{2} - 47 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(32*x-47,x, algorithm="maxima")

[Out]

16*x^2 - 47*x

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mupad [B]  time = 0.03, size = 7, normalized size = 0.35 \begin {gather*} x\,\left (16\,x-47\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32*x - 47,x)

[Out]

x*(16*x - 47)

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sympy [A]  time = 0.05, size = 7, normalized size = 0.35 \begin {gather*} 16 x^{2} - 47 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(32*x-47,x)

[Out]

16*x**2 - 47*x

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