3.41.47 $\int (8+6e^{6x}-4x)dx$

Optimal. Leaf size=13 $$e^{6x}-2(-2+x{)}^2$$

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.08, number of steps used = 2, number of rules used = 1, integrand size = 12, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.083, Rules used = {2194} $$\begin{array}{c}-2x^2+8x+e^{6x}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[8 + 6*E^(6*x) - 4*x,x]

[Out]

E^(6*x) + 8*x - 2*x^2

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =8x-2x^2+6\int e^{6x}dx\\ & =e^{6x}+8x-2x^2\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.08 $$\begin{array}{c}{e}^{6x}+8x-2x^2\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[8 + 6*E^(6*x) - 4*x,x]

[Out]

E^(6*x) + 8*x - 2*x^2

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fricas [A]  time = 1.24, size = 13, normalized size = 1.00 $$\begin{array}{c}-2x^2+8x+e^{\left(6x\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*exp(6*x)-4*x+8,x, algorithm="fricas")

[Out]

-2*x^2 + 8*x + e^(6*x)

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giac [A]  time = 0.19, size = 13, normalized size = 1.00 $$\begin{array}{c}-2x^2+8x+e^{\left(6x\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*exp(6*x)-4*x+8,x, algorithm="giac")

[Out]

-2*x^2 + 8*x + e^(6*x)

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maple [A]  time = 0.02, size = 14, normalized size = 1.08

method	result	size
derivativedivides	$8x-2x^2+{\mathrm{e}}^{6x}$	$14$
default	$8x-2x^2+{\mathrm{e}}^{6x}$	$14$
norman	$8x-2x^2+{\mathrm{e}}^{6x}$	$14$
risch	$8x-2x^2+{\mathrm{e}}^{6x}$	$14$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*exp(6*x)-4*x+8,x,method=_RETURNVERBOSE)

[Out]

8*x-2*x^2+exp(6*x)

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maxima [A]  time = 0.36, size = 13, normalized size = 1.00 $$\begin{array}{c}-2x^2+8x+e^{\left(6x\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*exp(6*x)-4*x+8,x, algorithm="maxima")

[Out]

-2*x^2 + 8*x + e^(6*x)

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mupad [B]  time = 2.99, size = 13, normalized size = 1.00 $$\begin{array}{c}8x+{\mathrm{e}}^{6x}-2x^2\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*exp(6*x) - 4*x + 8,x)

[Out]

8*x + exp(6*x) - 2*x^2

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sympy [A]  time = 0.07, size = 12, normalized size = 0.92 $$\begin{array}{c}-2x^2+8x+e^{6x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*exp(6*x)-4*x+8,x)

[Out]

-2*x**2 + 8*x + exp(6*x)

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