3.9.36 \(\int \frac {-25-3 e^{3 e^x+x}}{e^{3 e^x}+25 x} \, dx\)

Optimal. Leaf size=20 \[ 5-\log (2)-\log \left (e^{3 e^x}+25 x\right ) \]

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Rubi [A]  time = 0.07, antiderivative size = 14, normalized size of antiderivative = 0.70, number of steps used = 1, number of rules used = 1, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.037, Rules used = {6684} \begin {gather*} -\log \left (25 x+e^{3 e^x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-25 - 3*E^(3*E^x + x))/(E^(3*E^x) + 25*x),x]

[Out]

-Log[E^(3*E^x) + 25*x]

Rule 6684

Int[(u_)/(y_), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Simp[q*Log[RemoveContent[y, x]], x] /;  !Fa
lseQ[q]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\log \left (e^{3 e^x}+25 x\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 14, normalized size = 0.70 \begin {gather*} -\log \left (e^{3 e^x}+25 x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-25 - 3*E^(3*E^x + x))/(E^(3*E^x) + 25*x),x]

[Out]

-Log[E^(3*E^x) + 25*x]

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fricas [A]  time = 0.83, size = 18, normalized size = 0.90 \begin {gather*} x - \log \left (25 \, x e^{x} + e^{\left (x + 3 \, e^{x}\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*exp(x)*exp(3*exp(x))-25)/(exp(3*exp(x))+25*x),x, algorithm="fricas")

[Out]

x - log(25*x*e^x + e^(x + 3*e^x))

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giac [A]  time = 0.28, size = 12, normalized size = 0.60 \begin {gather*} -\log \left (25 \, x + e^{\left (3 \, e^{x}\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*exp(x)*exp(3*exp(x))-25)/(exp(3*exp(x))+25*x),x, algorithm="giac")

[Out]

-log(25*x + e^(3*e^x))

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maple [A]  time = 0.04, size = 13, normalized size = 0.65

method	result	size
norman	\(-\ln \left ({\mathrm e}^{3 \,{\mathrm e}^{x}}+25 x \right )\)	\(13\)
risch	\(-\ln \left ({\mathrm e}^{3 \,{\mathrm e}^{x}}+25 x \right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-3*exp(x)*exp(3*exp(x))-25)/(exp(3*exp(x))+25*x),x,method=_RETURNVERBOSE)

[Out]

-ln(exp(3*exp(x))+25*x)

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maxima [A]  time = 0.69, size = 12, normalized size = 0.60 \begin {gather*} -\log \left (25 \, x + e^{\left (3 \, e^{x}\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*exp(x)*exp(3*exp(x))-25)/(exp(3*exp(x))+25*x),x, algorithm="maxima")

[Out]

-log(25*x + e^(3*e^x))

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mupad [B]  time = 0.63, size = 12, normalized size = 0.60 \begin {gather*} -\ln \left (25\,x+{\mathrm {e}}^{3\,{\mathrm {e}}^x}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*exp(3*exp(x))*exp(x) + 25)/(25*x + exp(3*exp(x))),x)

[Out]

-log(25*x + exp(3*exp(x)))

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sympy [A]  time = 0.11, size = 12, normalized size = 0.60 \begin {gather*} - \log {\left (25 x + e^{3 e^{x}} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-3*exp(x)*exp(3*exp(x))-25)/(exp(3*exp(x))+25*x),x)

[Out]

-log(25*x + exp(3*exp(x)))

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