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

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

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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} $$\begin{array}{c}\frac{2x^3}{e^5}+2e^{3x}\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{2x^3}{e^5}+6\int e^{3x}dx\\ & =2e^{3x}+\frac{2x^3}{e^5}\end{array}\end{array}$$

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Mathematica [A]  time = 0.01, size = 22, normalized size = 1.38 $$\begin{array}{c}6(\frac{e^{3x}}{3}+\frac{x^3}{3e^5})\end{array}$$

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 $$\begin{array}{c}2(x^3+e^{(3x+5)})e^{(-5)}\end{array}$$

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 $$\begin{array}{c}2x^3{e}^{(-5)}+2e^{\left(3x\right)}\end{array}$$

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	$2x^3{\mathrm{e}}^{-5}+2{\mathrm{e}}^{3x}$	$15$
risch	$2x^3{\mathrm{e}}^{-5}+2{\mathrm{e}}^{3x}$	$15$
norman	$2x^3{\mathrm{e}}^{-5}+2{\mathrm{e}}^{3x}$	$17$

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 $$\begin{array}{c}2x^3{e}^{(-5)}+2e^{\left(3x\right)}\end{array}$$

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 $$\begin{array}{c}2{\mathrm{e}}^{3x}+2x^3{\mathrm{e}}^{-5}\end{array}$$

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 $$\begin{array}{c}\frac{2x^3}{e^5}+2e^{3x}\end{array}$$

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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