3.103.6 \(\int \frac {-3969-1024 e^{1024 x/3969}}{3969} \, dx\)

Optimal. Leaf size=14 \[ 4-e^{1024 x/3969}-x \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.93, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 2194} \begin {gather*} -x-e^{1024 x/3969} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-3969 - 1024*E^((1024*x)/3969))/3969,x]

[Out]

-E^((1024*x)/3969) - x

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, 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} &=\frac {\int \left (-3969-1024 e^{1024 x/3969}\right ) \, dx}{3969}\\ &=-x-\frac {1024 \int e^{1024 x/3969} \, dx}{3969}\\ &=-e^{1024 x/3969}-x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.93 \begin {gather*} -e^{1024 x/3969}-x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-3969 - 1024*E^((1024*x)/3969))/3969,x]

[Out]

-E^((1024*x)/3969) - x

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fricas [A]  time = 0.69, size = 10, normalized size = 0.71 \begin {gather*} -x - e^{\left (\frac {1024}{3969} \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1024/3969*exp(1024/3969*x)-1,x, algorithm="fricas")

[Out]

-x - e^(1024/3969*x)

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giac [A]  time = 0.14, size = 10, normalized size = 0.71 \begin {gather*} -x - e^{\left (\frac {1024}{3969} \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1024/3969*exp(1024/3969*x)-1,x, algorithm="giac")

[Out]

-x - e^(1024/3969*x)

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maple [A]  time = 0.02, size = 11, normalized size = 0.79

method	result	size
default	\(-x -{\mathrm e}^{\frac {1024 x}{3969}}\)	\(11\)
norman	\(-x -{\mathrm e}^{\frac {1024 x}{3969}}\)	\(11\)
risch	\(-x -{\mathrm e}^{\frac {1024 x}{3969}}\)	\(11\)
derivativedivides	\(-{\mathrm e}^{\frac {1024 x}{3969}}-\frac {3969 \ln \left ({\mathrm e}^{\frac {1024 x}{3969}}\right )}{1024}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1024/3969*exp(1024/3969*x)-1,x,method=_RETURNVERBOSE)

[Out]

-x-exp(1024/3969*x)

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maxima [A]  time = 0.35, size = 10, normalized size = 0.71 \begin {gather*} -x - e^{\left (\frac {1024}{3969} \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1024/3969*exp(1024/3969*x)-1,x, algorithm="maxima")

[Out]

-x - e^(1024/3969*x)

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mupad [B]  time = 7.01, size = 10, normalized size = 0.71 \begin {gather*} -x-{\mathrm {e}}^{\frac {1024\,x}{3969}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- (1024*exp((1024*x)/3969))/3969 - 1,x)

[Out]

- x - exp((1024*x)/3969)

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sympy [A]  time = 0.07, size = 8, normalized size = 0.57 \begin {gather*} - x - e^{\frac {1024 x}{3969}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1024/3969*exp(1024/3969*x)-1,x)

[Out]

-x - exp(1024*x/3969)

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