3.64.71 \(\int (-1+e+32 x) \, dx\)

Optimal. Leaf size=17 \[ 2-x+e x-4 \left (6-4 x^2\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.82, number of steps used = 1, number of rules used = 0, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 16 x^2-(1-e) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 + E + 32*x,x]

[Out]

-((1 - E)*x) + 16*x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-((1-e) x)+16 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.71 \begin {gather*} -x+e x+16 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + E + 32*x,x]

[Out]

-x + E*x + 16*x^2

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fricas [A]  time = 0.62, size = 13, normalized size = 0.76 \begin {gather*} 16 \, x^{2} + x e - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1)+32*x-1,x, algorithm="fricas")

[Out]

16*x^2 + x*e - x

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giac [A]  time = 0.12, size = 13, normalized size = 0.76 \begin {gather*} 16 \, x^{2} + x e - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1)+32*x-1,x, algorithm="giac")

[Out]

16*x^2 + x*e - x

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maple [A]  time = 0.04, size = 13, normalized size = 0.76

method	result	size
norman	\(16 x^{2}+\left ({\mathrm e}-1\right ) x\)	\(13\)
gosper	\(x \,{\mathrm e}+16 x^{2}-x\)	\(14\)
default	\(x \,{\mathrm e}+16 x^{2}-x\)	\(14\)
risch	\(x \,{\mathrm e}+16 x^{2}-x\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(1)+32*x-1,x,method=_RETURNVERBOSE)

[Out]

16*x^2+(exp(1)-1)*x

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maxima [A]  time = 0.37, size = 13, normalized size = 0.76 \begin {gather*} 16 \, x^{2} + x e - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1)+32*x-1,x, algorithm="maxima")

[Out]

16*x^2 + x*e - x

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mupad [B]  time = 4.10, size = 12, normalized size = 0.71 \begin {gather*} 16\,x^2+\left (\mathrm {e}-1\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32*x + exp(1) - 1,x)

[Out]

x*(exp(1) - 1) + 16*x^2

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sympy [A]  time = 0.05, size = 10, normalized size = 0.59 \begin {gather*} 16 x^{2} + x \left (-1 + e\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(1)+32*x-1,x)

[Out]

16*x**2 + x*(-1 + E)

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