3.34.97 \(\int (-2+e^{16} x) \, dx\)

Optimal. Leaf size=19 \[ 1+2 \left (9-x+\frac {e^{16} x^2}{4}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.74, number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {e^{16} x^2}{2}-2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2 + E^16*x,x]

[Out]

-2*x + (E^16*x^2)/2

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.74 \begin {gather*} -2 x+\frac {e^{16} x^2}{2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2 + E^16*x,x]

[Out]

-2*x + (E^16*x^2)/2

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fricas [A]  time = 0.60, size = 11, normalized size = 0.58 \begin {gather*} \frac {1}{2} \, x^{2} e^{16} - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*exp(16)-2,x, algorithm="fricas")

[Out]

1/2*x^2*e^16 - 2*x

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giac [A]  time = 0.18, size = 11, normalized size = 0.58 \begin {gather*} \frac {1}{2} \, x^{2} e^{16} - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*exp(16)-2,x, algorithm="giac")

[Out]

1/2*x^2*e^16 - 2*x

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maple [A]  time = 0.02, size = 12, normalized size = 0.63

method	result	size
gosper	\(\frac {x^{2} {\mathrm e}^{16}}{2}-2 x\)	\(12\)
default	\(\frac {x^{2} {\mathrm e}^{16}}{2}-2 x\)	\(12\)
norman	\(\frac {x^{2} {\mathrm e}^{16}}{2}-2 x\)	\(12\)
risch	\(\frac {x^{2} {\mathrm e}^{16}}{2}-2 x\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x*exp(16)-2,x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.34, size = 11, normalized size = 0.58 \begin {gather*} \frac {1}{2} \, x^{2} e^{16} - 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*exp(16)-2,x, algorithm="maxima")

[Out]

1/2*x^2*e^16 - 2*x

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mupad [B]  time = 0.03, size = 9, normalized size = 0.47 \begin {gather*} \frac {x\,\left (x\,{\mathrm {e}}^{16}-4\right )}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x*exp(16) - 2,x)

[Out]

(x*(x*exp(16) - 4))/2

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sympy [A]  time = 0.05, size = 10, normalized size = 0.53 \begin {gather*} \frac {x^{2} e^{16}}{2} - 2 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*exp(16)-2,x)

[Out]

x**2*exp(16)/2 - 2*x

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