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

Optimal. Leaf size=13 \[ x \left (6+e \left (\frac {19}{5}+2 x\right )\right ) \]

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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 {gather*} \frac {1}{200} e (20 x+19)^2+6 x \end {gather*}

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 {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int (30+e (19+20 x)) \, dx\\ &=6 x+\frac {1}{200} e (19+20 x)^2\\ \end {aligned} \end {gather*}

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

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 {gather*} \frac {1}{5} \, {\left (10 \, x^{2} + 19 \, x\right )} e + 6 \, x \end {gather*}

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 {gather*} \frac {1}{5} \, {\left (10 \, x^{2} + 19 \, x\right )} e + 6 \, x \end {gather*}

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	\(\frac {x \left (10 x \,{\mathrm e}+19 \,{\mathrm e}+30\right )}{5}\)	\(15\)
norman	\(\left (\frac {19 \,{\mathrm e}}{5}+6\right ) x +2 x^{2} {\mathrm e}\)	\(17\)
risch	\(2 x^{2} {\mathrm e}+\frac {19 x \,{\mathrm e}}{5}+6 x\)	\(17\)
default	\(\frac {{\mathrm e} \left (10 x^{2}+19 x \right )}{5}+6 x\)	\(18\)

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 {gather*} \frac {1}{5} \, {\left (10 \, x^{2} + 19 \, x\right )} e + 6 \, x \end {gather*}

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 {gather*} \frac {\left (20\,x+19\right )\,\left (\mathrm {e}\,\left (20\,x+19\right )+60\right )}{200} \end {gather*}

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 {gather*} 2 e x^{2} + x \left (6 + \frac {19 e}{5}\right ) \end {gather*}

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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