3.32.78 \(\int (3-16 e^{-3+4 x}) \, dx\)

Optimal. Leaf size=18 \[ -\frac {4}{e^4}-4 e^{-3+4 x}+3 x \]

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.72, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2194} \begin {gather*} 3 x-4 e^{4 x-3} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3 - 16*E^(-3 + 4*x),x]

[Out]

-4*E^(-3 + 4*x) + 3*x

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=3 x-16 \int e^{-3+4 x} \, dx\\ &=-4 e^{-3+4 x}+3 x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 13, normalized size = 0.72 \begin {gather*} -4 e^{-3+4 x}+3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3 - 16*E^(-3 + 4*x),x]

[Out]

-4*E^(-3 + 4*x) + 3*x

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fricas [A]  time = 0.61, size = 12, normalized size = 0.67 \begin {gather*} 3 \, x - 4 \, e^{\left (4 \, x - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-16*exp(4*x-3)+3,x, algorithm="fricas")

[Out]

3*x - 4*e^(4*x - 3)

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giac [A]  time = 0.24, size = 12, normalized size = 0.67 \begin {gather*} 3 \, x - 4 \, e^{\left (4 \, x - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-16*exp(4*x-3)+3,x, algorithm="giac")

[Out]

3*x - 4*e^(4*x - 3)

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maple [A]  time = 0.01, size = 13, normalized size = 0.72

method	result	size
default	\(3 x -4 \,{\mathrm e}^{4 x -3}\)	\(13\)
norman	\(3 x -4 \,{\mathrm e}^{4 x -3}\)	\(13\)
risch	\(3 x -4 \,{\mathrm e}^{4 x -3}\)	\(13\)
derivativedivides	\(-4 \,{\mathrm e}^{4 x -3}+\frac {3 \ln \left ({\mathrm e}^{4 x -3}\right )}{4}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-16*exp(4*x-3)+3,x,method=_RETURNVERBOSE)

[Out]

3*x-4*exp(4*x-3)

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maxima [A]  time = 0.35, size = 12, normalized size = 0.67 \begin {gather*} 3 \, x - 4 \, e^{\left (4 \, x - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-16*exp(4*x-3)+3,x, algorithm="maxima")

[Out]

3*x - 4*e^(4*x - 3)

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mupad [B]  time = 0.07, size = 12, normalized size = 0.67 \begin {gather*} 3\,x-4\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{-3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3 - 16*exp(4*x - 3),x)

[Out]

3*x - 4*exp(4*x)*exp(-3)

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sympy [A]  time = 0.07, size = 10, normalized size = 0.56 \begin {gather*} 3 x - 4 e^{4 x - 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-16*exp(4*x-3)+3,x)

[Out]

3*x - 4*exp(4*x - 3)

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