3.63.27 \(\int \frac {1}{13} (-39+10 e^{5 x}) \, dx\)

Optimal. Leaf size=14 \[ -2+\frac {2 e^{5 x}}{13}-3 x \]

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.93, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2194} \begin {gather*} \frac {2 e^{5 x}}{13}-3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-39 + 10*E^(5*x))/13,x]

[Out]

(2*E^(5*x))/13 - 3*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 {1}{13} \int \left (-39+10 e^{5 x}\right ) \, dx\\ &=-3 x+\frac {10}{13} \int e^{5 x} \, dx\\ &=\frac {2 e^{5 x}}{13}-3 x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.93 \begin {gather*} \frac {2 e^{5 x}}{13}-3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-39 + 10*E^(5*x))/13,x]

[Out]

(2*E^(5*x))/13 - 3*x

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fricas [A]  time = 0.57, size = 10, normalized size = 0.71 \begin {gather*} -3 \, x + \frac {2}{13} \, e^{\left (5 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10/13*exp(5*x)-3,x, algorithm="fricas")

[Out]

-3*x + 2/13*e^(5*x)

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giac [A]  time = 0.23, size = 10, normalized size = 0.71 \begin {gather*} -3 \, x + \frac {2}{13} \, e^{\left (5 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10/13*exp(5*x)-3,x, algorithm="giac")

[Out]

-3*x + 2/13*e^(5*x)

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maple [A]  time = 0.03, size = 11, normalized size = 0.79

method	result	size
default	\(-3 x +\frac {2 \,{\mathrm e}^{5 x}}{13}\)	\(11\)
norman	\(-3 x +\frac {2 \,{\mathrm e}^{5 x}}{13}\)	\(11\)
risch	\(-3 x +\frac {2 \,{\mathrm e}^{5 x}}{13}\)	\(11\)
derivativedivides	\(\frac {2 \,{\mathrm e}^{5 x}}{13}-\frac {3 \ln \left ({\mathrm e}^{5 x}\right )}{5}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10/13*exp(5*x)-3,x,method=_RETURNVERBOSE)

[Out]

-3*x+2/13*exp(5*x)

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maxima [A]  time = 0.35, size = 10, normalized size = 0.71 \begin {gather*} -3 \, x + \frac {2}{13} \, e^{\left (5 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10/13*exp(5*x)-3,x, algorithm="maxima")

[Out]

-3*x + 2/13*e^(5*x)

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mupad [B]  time = 0.05, size = 10, normalized size = 0.71 \begin {gather*} \frac {2\,{\mathrm {e}}^{5\,x}}{13}-3\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((10*exp(5*x))/13 - 3,x)

[Out]

(2*exp(5*x))/13 - 3*x

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sympy [A]  time = 0.07, size = 10, normalized size = 0.71 \begin {gather*} - 3 x + \frac {2 e^{5 x}}{13} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10/13*exp(5*x)-3,x)

[Out]

-3*x + 2*exp(5*x)/13

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