3.39.34 \(\int \frac {e^6-\frac {35 x^{4/3}}{e^5}}{e^6} \, dx\)

Optimal. Leaf size=12 \[ x-\frac {15 x^{7/3}}{e^{11}} \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {12} \begin {gather*} x-\frac {15 x^{7/3}}{e^{11}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^6 - (35*x^(4/3))/E^5)/E^6,x]

[Out]

x - (15*x^(7/3))/E^11

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (e^6-\frac {35 x^{4/3}}{e^5}\right ) \, dx}{e^6}\\ &=x-\frac {15 x^{7/3}}{e^{11}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} x-\frac {15 x^{7/3}}{e^{11}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^6 - (35*x^(4/3))/E^5)/E^6,x]

[Out]

x - (15*x^(7/3))/E^11

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fricas [A]  time = 0.59, size = 15, normalized size = 1.25 \begin {gather*} -{\left (15 \, x^{\frac {7}{3}} - x e^{11}\right )} e^{\left (-11\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-35*x^(1/3)*exp(log(x)-5)+exp(2)*exp(4))/exp(2)/exp(4),x, algorithm="fricas")

[Out]

-(15*x^(7/3) - x*e^11)*e^(-11)

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giac [A]  time = 0.12, size = 17, normalized size = 1.42 \begin {gather*} -{\left (15 \, x^{\frac {7}{3}} e^{\left (-5\right )} - x e^{6}\right )} e^{\left (-6\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-35*x^(1/3)*exp(log(x)-5)+exp(2)*exp(4))/exp(2)/exp(4),x, algorithm="giac")

[Out]

-(15*x^(7/3)*e^(-5) - x*e^6)*e^(-6)

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maple [A]  time = 0.08, size = 24, normalized size = 2.00

method	result	size
default	\({\mathrm e}^{-2} {\mathrm e}^{-4} \left ({\mathrm e}^{2} {\mathrm e}^{4} x -15 x^{\frac {7}{3}} {\mathrm e}^{-5}\right )\)	\(24\)
derivativedivides	\(3 \,{\mathrm e}^{-2} {\mathrm e}^{-4} \left (\frac {{\mathrm e}^{2} {\mathrm e}^{4} x}{3}-5 x^{\frac {7}{3}} {\mathrm e}^{-5}\right )\)	\(26\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-35*x^(1/3)*exp(ln(x)-5)+exp(2)*exp(4))/exp(2)/exp(4),x,method=_RETURNVERBOSE)

[Out]

1/exp(2)/exp(4)*(exp(2)*exp(4)*x-15*x^(7/3)*exp(-5))

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maxima [A]  time = 0.38, size = 17, normalized size = 1.42 \begin {gather*} -{\left (15 \, x^{\frac {7}{3}} e^{\left (-5\right )} - x e^{6}\right )} e^{\left (-6\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-35*x^(1/3)*exp(log(x)-5)+exp(2)*exp(4))/exp(2)/exp(4),x, algorithm="maxima")

[Out]

-(15*x^(7/3)*e^(-5) - x*e^6)*e^(-6)

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mupad [B]  time = 2.23, size = 9, normalized size = 0.75 \begin {gather*} x-15\,x^{7/3}\,{\mathrm {e}}^{-11} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-6)*(exp(6) - 35*x^(1/3)*exp(log(x) - 5)),x)

[Out]

x - 15*x^(7/3)*exp(-11)

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sympy [A]  time = 0.59, size = 17, normalized size = 1.42 \begin {gather*} \frac {- \frac {15 x^{\frac {7}{3}}}{e^{5}} + x e^{6}}{e^{6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-35*x**(1/3)*exp(ln(x)-5)+exp(2)*exp(4))/exp(2)/exp(4),x)

[Out]

(-15*x**(7/3)*exp(-5) + x*exp(6))*exp(-6)

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