3.12.28 \(\int -\frac {180}{3+e^{5/4}} \, dx\)

Optimal. Leaf size=20 \[ 9 \left (-2+\frac {20 (81-x)}{3+e^{5/4}}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.60, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {8} \begin {gather*} -\frac {180 x}{3+e^{5/4}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-180/(3 + E^(5/4)),x]

[Out]

(-180*x)/(3 + E^(5/4))

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {180 x}{3+e^{5/4}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.60 \begin {gather*} -\frac {180 x}{3+e^{5/4}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-180/(3 + E^(5/4)),x]

[Out]

(-180*x)/(3 + E^(5/4))

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fricas [A]  time = 0.53, size = 9, normalized size = 0.45 \begin {gather*} -\frac {180 \, x}{e^{\frac {5}{4}} + 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-180/(exp(5/4)+3),x, algorithm="fricas")

[Out]

-180*x/(e^(5/4) + 3)

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giac [A]  time = 0.62, size = 9, normalized size = 0.45 \begin {gather*} -\frac {180 \, x}{e^{\frac {5}{4}} + 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-180/(exp(5/4)+3),x, algorithm="giac")

[Out]

-180*x/(e^(5/4) + 3)

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maple [A]  time = 0.01, size = 10, normalized size = 0.50

method	result	size
default	\(-\frac {180 x}{{\mathrm e}^{\frac {5}{4}}+3}\)	\(10\)
norman	\(-\frac {180 x}{{\mathrm e}^{\frac {5}{4}}+3}\)	\(10\)
risch	\(-\frac {180 x}{{\mathrm e}^{\frac {5}{4}}+3}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-180/(exp(5/4)+3),x,method=_RETURNVERBOSE)

[Out]

-180/(exp(5/4)+3)*x

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maxima [A]  time = 0.75, size = 9, normalized size = 0.45 \begin {gather*} -\frac {180 \, x}{e^{\frac {5}{4}} + 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-180/(exp(5/4)+3),x, algorithm="maxima")

[Out]

-180*x/(e^(5/4) + 3)

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mupad [B]  time = 0.00, size = 9, normalized size = 0.45 \begin {gather*} -\frac {180\,x}{{\mathrm {e}}^{5/4}+3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-180/(exp(5/4) + 3),x)

[Out]

-(180*x)/(exp(5/4) + 3)

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sympy [A]  time = 0.04, size = 10, normalized size = 0.50 \begin {gather*} - \frac {180 x}{3 + e^{\frac {5}{4}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-180/(exp(5/4)+3),x)

[Out]

-180*x/(3 + exp(5/4))

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