\(\int -\frac {180}{3+e^{5/4}} \, dx\) [1128]

Optimal result

Integrand size = 11, antiderivative size = 20 \[ \int -\frac {180}{3+e^{5/4}} \, dx=9 \left (-2+\frac {20 (81-x)}{3+e^{5/4}}\right ) \]

[Out]

180/(exp(5/4)+3)*(81-x)-18

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.60, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {8} \[ \int -\frac {180}{3+e^{5/4}} \, dx=-\frac {180 x}{3+e^{5/4}} \]

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.60 \[ \int -\frac {180}{3+e^{5/4}} \, dx=-\frac {180 x}{3+e^{5/4}} \]

[In]

Integrate[-180/(3 + E^(5/4)),x]

[Out]

(-180*x)/(3 + E^(5/4))

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 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	\(-\frac {180 x}{{\mathrm e}^{\frac {5}{4}}+3}\)	\(10\)
parallelrisch	\(-\frac {180 x}{{\mathrm e}^{\frac {5}{4}}+3}\)	\(10\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.45 \[ \int -\frac {180}{3+e^{5/4}} \, dx=-\frac {180 \, x}{e^{\frac {5}{4}} + 3} \]

[In]

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

[Out]

-180*x/(e^(5/4) + 3)

Sympy [A] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.50 \[ \int -\frac {180}{3+e^{5/4}} \, dx=- \frac {180 x}{3 + e^{\frac {5}{4}}} \]

[In]

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

[Out]

-180*x/(3 + exp(5/4))

Maxima [A] (verification not implemented)

none

Time = 0.17 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.45 \[ \int -\frac {180}{3+e^{5/4}} \, dx=-\frac {180 \, x}{e^{\frac {5}{4}} + 3} \]

[In]

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

[Out]

-180*x/(e^(5/4) + 3)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.45 \[ \int -\frac {180}{3+e^{5/4}} \, dx=-\frac {180 \, x}{e^{\frac {5}{4}} + 3} \]

[In]

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

[Out]

-180*x/(e^(5/4) + 3)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.45 \[ \int -\frac {180}{3+e^{5/4}} \, dx=-\frac {180\,x}{{\mathrm {e}}^{5/4}+3} \]

[In]

int(-180/(exp(5/4) + 3),x)

[Out]

-(180*x)/(exp(5/4) + 3)