3.41.66 $\int \frac{1}{5}(30+e(19+20x))dx$

Optimal. Leaf size=13 $$x(6+e(\frac{19}{5}+2x))$$

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Rubi [A]  time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.23, number of steps used = 2, number of rules used = 1, integrand size = 13, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.077, Rules used = {12} $$\begin{array}{c}\frac{1}{200}e(20x+19{)}^2+6x\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(30 + E*(19 + 20*x))/5,x]

[Out]

6*x + (E*(19 + 20*x)^2)/200

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{1}{5}\int (30+e(19+20x))dx\\ & =6x+\frac{1}{200}e(19+20x{)}^2\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 16, normalized size = 1.23 $$\begin{array}{c}6x+\frac{19ex}{5}+2e{x}^2\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(30 + E*(19 + 20*x))/5,x]

[Out]

6*x + (19*E*x)/5 + 2*E*x^2

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fricas [A]  time = 0.63, size = 17, normalized size = 1.31 $$\begin{array}{c}\frac{1}{5}(10x^2+19x)e+6x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(20*x+19)*exp(1)+6,x, algorithm="fricas")

[Out]

1/5*(10*x^2 + 19*x)*e + 6*x

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giac [A]  time = 0.15, size = 17, normalized size = 1.31 $$\begin{array}{c}\frac{1}{5}(10x^2+19x)e+6x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(20*x+19)*exp(1)+6,x, algorithm="giac")

[Out]

1/5*(10*x^2 + 19*x)*e + 6*x

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maple [A]  time = 0.02, size = 15, normalized size = 1.15

method	result	size
gosper	$\frac{x(10x\mathrm{e}+19\mathrm{e}+30)}{5}$	$15$
norman	$(\frac{19\mathrm{e}}{5}+6)x+2x^2\mathrm{e}$	$17$
risch	$2x^2\mathrm{e}+\frac{19x\mathrm{e}}{5}+6x$	$17$
default	$\frac{\mathrm{e}(10x^2+19x)}{5}+6x$	$18$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/5*(20*x+19)*exp(1)+6,x,method=_RETURNVERBOSE)

[Out]

1/5*x*(10*x*exp(1)+19*exp(1)+30)

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maxima [A]  time = 0.36, size = 17, normalized size = 1.31 $$\begin{array}{c}\frac{1}{5}(10x^2+19x)e+6x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(20*x+19)*exp(1)+6,x, algorithm="maxima")

[Out]

1/5*(10*x^2 + 19*x)*e + 6*x

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mupad [B]  time = 0.07, size = 17, normalized size = 1.31 $$\begin{array}{c}\frac{(20x+19)(\mathrm{e}(20x+19)+60)}{200}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(1)*(20*x + 19))/5 + 6,x)

[Out]

((20*x + 19)*(exp(1)*(20*x + 19) + 60))/200

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sympy [A]  time = 0.05, size = 17, normalized size = 1.31 $$\begin{array}{c}2e{x}^2+x(6+\frac{19e}{5})\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(20*x+19)*exp(1)+6,x)

[Out]

2*E*x**2 + x*(6 + 19*E/5)

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