3.85.81 $\int \frac{6250+e^{2e^{8x/5}}(-5-16e^{8x/5}x)}{3125}dx$

Optimal. Leaf size=20 $$2x-\frac{1}{625}{e}^{2e^{8x/5}}x$$

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Rubi [A]  time = 0.02, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 30, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.067, Rules used = {12, 2288} $$\begin{array}{c}2x-\frac{1}{625}{e}^{2e^{8x/5}}x\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(6250 + E^(2*E^((8*x)/5))*(-5 - 16*E^((8*x)/5)*x))/3125,x]

[Out]

2*x - (E^(2*E^((8*x)/5))*x)/625

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{\int (6250+e^{2e^{8x/5}}(-5-16e^{8x/5}x))dx}{3125}\\ & =2x+\frac{\int e^{2e^{8x/5}}(-5-16e^{8x/5}x)dx}{3125}\\ & =2x-\frac{1}{625}{e}^{2e^{8x/5}}x\end{array}\end{array}$$

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Mathematica [A]  time = 0.02, size = 20, normalized size = 1.00 $$\begin{array}{c}2x-\frac{1}{625}{e}^{2e^{8x/5}}x\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(6250 + E^(2*E^((8*x)/5))*(-5 - 16*E^((8*x)/5)*x))/3125,x]

[Out]

2*x - (E^(2*E^((8*x)/5))*x)/625

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fricas [A]  time = 0.46, size = 14, normalized size = 0.70 $$\begin{array}{c}-\frac{1}{625}x{e}^{\left(2e^{\left(\frac{8}{5}x\right)}\right)}+2x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3125*(-16*x*exp(8/5*x)-5)*exp(exp(8/5*x))^2+2,x, algorithm="fricas")

[Out]

-1/625*x*e^(2*e^(8/5*x)) + 2*x

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\int -\frac{1}{3125}(16x{e}^{\left(\frac{8}{5}x\right)}+5)e^{\left(2e^{\left(\frac{8}{5}x\right)}\right)}+2dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3125*(-16*x*exp(8/5*x)-5)*exp(exp(8/5*x))^2+2,x, algorithm="giac")

[Out]

integrate(-1/3125*(16*x*e^(8/5*x) + 5)*e^(2*e^(8/5*x)) + 2, x)

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maple [A]  time = 0.05, size = 15, normalized size = 0.75

method	result	size
default	$2x-\frac{{\mathrm{e}}^{2{\mathrm{e}}^{\frac{8x}{5}}}x}{625}$	$15$
norman	$2x-\frac{{\mathrm{e}}^{2{\mathrm{e}}^{\frac{8x}{5}}}x}{625}$	$15$
risch	$2x-\frac{{\mathrm{e}}^{2{\mathrm{e}}^{\frac{8x}{5}}}x}{625}$	$15$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/3125*(-16*x*exp(8/5*x)-5)*exp(exp(8/5*x))^2+2,x,method=_RETURNVERBOSE)

[Out]

2*x-1/625*exp(exp(8/5*x))^2*x

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}-\frac{1}{625}x{e}^{\left(2e^{\left(\frac{8}{5}x\right)}\right)}+2x-\frac{1}{1000}\mathrm{E}\mathrm{i}\left(2e^{\left(\frac{8}{5}x\right)}\right)+\frac{1}{625}\int e^{\left(2e^{\left(\frac{8}{5}x\right)}\right)}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3125*(-16*x*exp(8/5*x)-5)*exp(exp(8/5*x))^2+2,x, algorithm="maxima")

[Out]

-1/625*x*e^(2*e^(8/5*x)) + 2*x - 1/1000*Ei(2*e^(8/5*x)) + 1/625*integrate(e^(2*e^(8/5*x)), x)

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mupad [B]  time = 0.06, size = 12, normalized size = 0.60 $$\begin{array}{c}-\frac{x({\mathrm{e}}^{2{\mathrm{e}}^{\frac{8x}{5}}}-1250)}{625}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2 - (exp(2*exp((8*x)/5))*(16*x*exp((8*x)/5) + 5))/3125,x)

[Out]

-(x*(exp(2*exp((8*x)/5)) - 1250))/625

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sympy [A]  time = 0.14, size = 15, normalized size = 0.75 $$\begin{array}{c}-\frac{x{e}^{2e^{\frac{8x}{5}}}}{625}+2x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3125*(-16*x*exp(8/5*x)-5)*exp(exp(8/5*x))**2+2,x)

[Out]

-x*exp(2*exp(8*x/5))/625 + 2*x

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