3.35.35 \(\int (-\frac {320 e^{10}}{x^5}-\frac {320 e^5}{x^3}) \, dx\)

Optimal. Leaf size=13 \[ 80 \left (1+\frac {e^5}{x^2}\right )^2 \]

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Rubi [A]  time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.31, number of steps used = 1, number of rules used = 0, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \frac {80 e^{10}}{x^4}+\frac {160 e^5}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-320*E^10)/x^5 - (320*E^5)/x^3,x]

[Out]

(80*E^10)/x^4 + (160*E^5)/x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {80 e^{10}}{x^4}+\frac {160 e^5}{x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 23, normalized size = 1.77 \begin {gather*} -320 e^5 \left (-\frac {e^5}{4 x^4}-\frac {1}{2 x^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-320*E^10)/x^5 - (320*E^5)/x^3,x]

[Out]

-320*E^5*(-1/4*E^5/x^4 - 1/(2*x^2))

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fricas [A]  time = 0.50, size = 15, normalized size = 1.15 \begin {gather*} \frac {80 \, {\left (2 \, x^{2} e^{5} + e^{10}\right )}}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-320*x*exp(-3*log(x)+5)^2-320*exp(-3*log(x)+5),x, algorithm="fricas")

[Out]

80*(2*x^2*e^5 + e^10)/x^4

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giac [A]  time = 0.24, size = 15, normalized size = 1.15 \begin {gather*} \frac {160 \, e^{5}}{x^{2}} + \frac {80 \, e^{10}}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-320*x*exp(-3*log(x)+5)^2-320*exp(-3*log(x)+5),x, algorithm="giac")

[Out]

160*e^5/x^2 + 80*e^10/x^4

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maple [A]  time = 0.02, size = 16, normalized size = 1.23

method	result	size
default	\(\frac {80 \,{\mathrm e}^{10}}{x^{4}}+\frac {160 \,{\mathrm e}^{5}}{x^{2}}\)	\(16\)
risch	\(\frac {80 \,{\mathrm e}^{10}}{x^{4}}+\frac {160 \,{\mathrm e}^{5}}{x^{2}}\)	\(16\)
norman	\(\frac {80 \,{\mathrm e}^{10}+160 x^{2} {\mathrm e}^{5}}{x^{4}}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-320*x*exp(-3*ln(x)+5)^2-320*exp(-3*ln(x)+5),x,method=_RETURNVERBOSE)

[Out]

80*exp(10)/x^4+160*exp(5)/x^2

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maxima [A]  time = 0.41, size = 15, normalized size = 1.15 \begin {gather*} \frac {160 \, e^{5}}{x^{2}} + \frac {80 \, e^{10}}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-320*x*exp(-3*log(x)+5)^2-320*exp(-3*log(x)+5),x, algorithm="maxima")

[Out]

160*e^5/x^2 + 80*e^10/x^4

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mupad [B]  time = 0.06, size = 15, normalized size = 1.15 \begin {gather*} \frac {80\,{\mathrm {e}}^5\,\left (2\,x^2+{\mathrm {e}}^5\right )}{x^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- 320*exp(5 - 3*log(x)) - 320*x*exp(10 - 6*log(x)),x)

[Out]

(80*exp(5)*(exp(5) + 2*x^2))/x^4

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sympy [A]  time = 0.14, size = 19, normalized size = 1.46 \begin {gather*} - \frac {- 160 x^{2} e^{5} - 80 e^{10}}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-320*x*exp(-3*ln(x)+5)**2-320*exp(-3*ln(x)+5),x)

[Out]

-(-160*x**2*exp(5) - 80*exp(10))/x**4

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