3.35.78 \(\int \frac {-6 e^{22}+25 e^4 x}{x^7} \, dx\)

Optimal. Leaf size=14 \[ \frac {e^4 \left (e^{18}-5 x\right )}{x^6} \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.14, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {43} \begin {gather*} \frac {e^{22}}{x^6}-\frac {5 e^4}{x^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-6*E^22 + 25*E^4*x)/x^7,x]

[Out]

E^22/x^6 - (5*E^4)/x^5

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {6 e^{22}}{x^7}+\frac {25 e^4}{x^6}\right ) \, dx\\ &=\frac {e^{22}}{x^6}-\frac {5 e^4}{x^5}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 16, normalized size = 1.14 \begin {gather*} \frac {e^{22}}{x^6}-\frac {5 e^4}{x^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-6*E^22 + 25*E^4*x)/x^7,x]

[Out]

E^22/x^6 - (5*E^4)/x^5

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fricas [A]  time = 0.69, size = 15, normalized size = 1.07 \begin {gather*} -\frac {5 \, x e^{4} - e^{22}}{x^{6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-6*exp(4)*exp(9)^2+25*x*exp(4))/x^7,x, algorithm="fricas")

[Out]

-(5*x*e^4 - e^22)/x^6

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giac [A]  time = 0.27, size = 15, normalized size = 1.07 \begin {gather*} -\frac {5 \, x e^{4} - e^{22}}{x^{6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-6*exp(4)*exp(9)^2+25*x*exp(4))/x^7,x, algorithm="giac")

[Out]

-(5*x*e^4 - e^22)/x^6

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maple [A]  time = 0.04, size = 13, normalized size = 0.93

method	result	size
risch	\(\frac {{\mathrm e}^{22}-5 x \,{\mathrm e}^{4}}{x^{6}}\)	\(13\)
gosper	\(\frac {{\mathrm e}^{4} \left ({\mathrm e}^{18}-5 x \right )}{x^{6}}\)	\(15\)
default	\({\mathrm e}^{4} \left (-\frac {5}{x^{5}}+\frac {{\mathrm e}^{18}}{x^{6}}\right )\)	\(16\)
norman	\(\frac {{\mathrm e}^{4} {\mathrm e}^{18}-5 x \,{\mathrm e}^{4}}{x^{6}}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-6*exp(4)*exp(9)^2+25*x*exp(4))/x^7,x,method=_RETURNVERBOSE)

[Out]

(exp(22)-5*x*exp(4))/x^6

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maxima [A]  time = 0.94, size = 15, normalized size = 1.07 \begin {gather*} -\frac {5 \, x e^{4} - e^{22}}{x^{6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-6*exp(4)*exp(9)^2+25*x*exp(4))/x^7,x, algorithm="maxima")

[Out]

-(5*x*e^4 - e^22)/x^6

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mupad [B]  time = 1.94, size = 15, normalized size = 1.07 \begin {gather*} -\frac {{\mathrm {e}}^4\,\left (5\,x-{\mathrm {e}}^{18}\right )}{x^6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(6*exp(22) - 25*x*exp(4))/x^7,x)

[Out]

-(exp(4)*(5*x - exp(18)))/x^6

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sympy [A]  time = 0.14, size = 12, normalized size = 0.86 \begin {gather*} \frac {- 5 x e^{4} + e^{22}}{x^{6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-6*exp(4)*exp(9)**2+25*x*exp(4))/x**7,x)

[Out]

(-5*x*exp(4) + exp(22))/x**6

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