3.69.99 \(\int (6 e^{3 x}+\frac {6 x^2}{e^5}) \, dx\)

Optimal. Leaf size=16 \[ 2 \left (1+e^{3 x}+\frac {x^3}{e^5}\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, 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 = {2194} \begin {gather*} \frac {2 x^3}{e^5}+2 e^{3 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[6*E^(3*x) + (6*x^2)/E^5,x]

[Out]

2*E^(3*x) + (2*x^3)/E^5

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {2 x^3}{e^5}+6 \int e^{3 x} \, dx\\ &=2 e^{3 x}+\frac {2 x^3}{e^5}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 22, normalized size = 1.38 \begin {gather*} 6 \left (\frac {e^{3 x}}{3}+\frac {x^3}{3 e^5}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[6*E^(3*x) + (6*x^2)/E^5,x]

[Out]

6*(E^(3*x)/3 + x^3/(3*E^5))

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fricas [A]  time = 0.56, size = 14, normalized size = 0.88 \begin {gather*} 2 \, {\left (x^{3} + e^{\left (3 \, x + 5\right )}\right )} e^{\left (-5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x*exp(log(x)-5)+6*exp(3*x),x, algorithm="fricas")

[Out]

2*(x^3 + e^(3*x + 5))*e^(-5)

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giac [A]  time = 0.36, size = 14, normalized size = 0.88 \begin {gather*} 2 \, x^{3} e^{\left (-5\right )} + 2 \, e^{\left (3 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x*exp(log(x)-5)+6*exp(3*x),x, algorithm="giac")

[Out]

2*x^3*e^(-5) + 2*e^(3*x)

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maple [A]  time = 0.03, size = 15, normalized size = 0.94

method	result	size
default	\(2 x^{3} {\mathrm e}^{-5}+2 \,{\mathrm e}^{3 x}\)	\(15\)
risch	\(2 x^{3} {\mathrm e}^{-5}+2 \,{\mathrm e}^{3 x}\)	\(15\)
norman	\(2 x^{3} {\mathrm e}^{-5}+2 \,{\mathrm e}^{3 x}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*x*exp(ln(x)-5)+6*exp(3*x),x,method=_RETURNVERBOSE)

[Out]

2*x^3*exp(-5)+2*exp(3*x)

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maxima [A]  time = 0.35, size = 14, normalized size = 0.88 \begin {gather*} 2 \, x^{3} e^{\left (-5\right )} + 2 \, e^{\left (3 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x*exp(log(x)-5)+6*exp(3*x),x, algorithm="maxima")

[Out]

2*x^3*e^(-5) + 2*e^(3*x)

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mupad [B]  time = 4.08, size = 14, normalized size = 0.88 \begin {gather*} 2\,{\mathrm {e}}^{3\,x}+2\,x^3\,{\mathrm {e}}^{-5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2*exp(3*x) + 2*x^3*exp(-5)

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sympy [A]  time = 0.09, size = 14, normalized size = 0.88 \begin {gather*} \frac {2 x^{3}}{e^{5}} + 2 e^{3 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x*exp(ln(x)-5)+6*exp(3*x),x)

[Out]

2*x**3*exp(-5) + 2*exp(3*x)

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