∫ −162e−1+3e3+e 18 ________95+9x + 18___95+9x _________________________________

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Rubi [A] time = 0.32, antiderivative size = 20, normalized size of antiderivative = 0.91, number of steps used = 6, number of rules used = 5, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.116, Rules used = {12, 27, 6715, 2282, 2194} \begin {gather*} e^{e^{\frac {18}{9 x+95}}-1+3 e^3} \end {gather*}

Int[(-162*E^(-1 + 3*E^3 + E^(18/(95 + 9*x)) + 18/(95 + 9*x)))/(9025 + 1710*x + 81*x^2),x]

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

Int[(u_.)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[u*Cancel[(b/2 + c*x)^(2*p)/c^p], x] /; Fr

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre

Int[u_, x_Symbol] :> With[{v = FunctionOfExponential[u, x]}, Dist[v/D[v, x], Subst[Int[FunctionOfExponentialFu

nction[u, x]/x, x], x, v], x]] /; FunctionOfExponentialQ[u, x] && !MatchQ[u, (w_)*((a_.)*(v_)^(n_))^(m_) /; F

reeQ[{a, m, n}, x] && IntegerQ[m*n]] && !MatchQ[u, E^((c_.)*((a_.) + (b_.)*x))*(F_)[v_] /; FreeQ[{a, b, c}, x

Int[(u_)*(x_)^(m_.), x_Symbol] :> Dist[1/(m + 1), Subst[Int[SubstFor[x^(m + 1), u, x], x], x, x^(m + 1)], x] /

\begin {gather*} \begin {aligned} \text {integral} &=-\left (162 \int \frac {e^{-1+3 e^3+e^{\frac {18}{95+9 x}}+\frac {18}{95+9 x}}}{9025+1710 x+81 x^2} \, dx\right )\\ &=-\left (162 \int \frac {e^{-1+3 e^3+e^{\frac {18}{95+9 x}}+\frac {18}{95+9 x}}}{(95+9 x)^2} \, dx\right )\\ &=-\left (18 \operatorname {Subst}\left (\int \frac {e^{-1+3 e^3+e^{18/x}+\frac {18}{x}}}{x^2} \, dx,x,95+9 x\right )\right )\\ &=18 \operatorname {Subst}\left (\int e^{-1+3 e^3+e^{18 x}+18 x} \, dx,x,\frac {1}{95+9 x}\right )\\ &=\operatorname {Subst}\left (\int e^{-1+3 e^3+x} \, dx,x,e^{\frac {18}{95+9 x}}\right )\\ &=e^{-1+3 e^3+e^{\frac {18}{95+9 x}}}\\ \end {aligned} \end {gather*}

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Mathematica [A] time = 0.12, size = 20, normalized size = 0.91 \begin {gather*} e^{-1+3 e^3+e^{\frac {18}{95+9 x}}} \end {gather*}

Integrate[(-162*E^(-1 + 3*E^3 + E^(18/(95 + 9*x)) + 18/(95 + 9*x)))/(9025 + 1710*x + 81*x^2),x]

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fricas [B] time = 0.64, size = 49, normalized size = 2.23 \begin {gather*} e^{\left (\frac {3 \, {\left (9 \, x + 95\right )} e^{3} + {\left (9 \, x + 95\right )} e^{\left (\frac {18}{9 \, x + 95}\right )} - 9 \, x - 77}{9 \, x + 95} - \frac {18}{9 \, x + 95}\right )} \end {gather*}

integrate(-162*exp(18/(9*x+95))*exp(3*exp(3))*exp(exp(18/(9*x+95))-1)/(81*x^2+1710*x+9025),x, algorithm="frica

e^((3*(9*x + 95)*e^3 + (9*x + 95)*e^(18/(9*x + 95)) - 9*x - 77)/(9*x + 95) - 18/(9*x + 95))

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giac [B] time = 0.27, size = 54, normalized size = 2.45 \begin {gather*} e^{\left (\frac {855 \, x e^{\left (\frac {18}{9 \, x + 95}\right )} - 162 \, x + 9025 \, e^{\left (\frac {18}{9 \, x + 95}\right )}}{95 \, {\left (9 \, x + 95\right )}} - \frac {18}{9 \, x + 95} + 3 \, e^{3} - \frac {77}{95}\right )} \end {gather*}

integrate(-162*exp(18/(9*x+95))*exp(3*exp(3))*exp(exp(18/(9*x+95))-1)/(81*x^2+1710*x+9025),x, algorithm="giac"

e^(1/95*(855*x*e^(18/(9*x + 95)) - 162*x + 9025*e^(18/(9*x + 95)))/(9*x + 95) - 18/(9*x + 95) + 3*e^3 - 77/95)

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method	result	size

risch	\({\mathrm e}^{3 \,{\mathrm e}^{3}+{\mathrm e}^{\frac {18}{9 x +95}}-1}\)	\(18\)
norman	\(\frac {95 \,{\mathrm e}^{3 \,{\mathrm e}^{3}} {\mathrm e}^{{\mathrm e}^{\frac {18}{9 x +95}}-1}+9 \,{\mathrm e}^{3 \,{\mathrm e}^{3}} x \,{\mathrm e}^{{\mathrm e}^{\frac {18}{9 x +95}}-1}}{9 x +95}\)	\(51\)

int(-162*exp(18/(9*x+95))*exp(3*exp(3))*exp(exp(18/(9*x+95))-1)/(81*x^2+1710*x+9025),x,method=_RETURNVERBOSE)

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maxima [A] time = 0.39, size = 17, normalized size = 0.77 \begin {gather*} e^{\left (3 \, e^{3} + e^{\left (\frac {18}{9 \, x + 95}\right )} - 1\right )} \end {gather*}

integrate(-162*exp(18/(9*x+95))*exp(3*exp(3))*exp(exp(18/(9*x+95))-1)/(81*x^2+1710*x+9025),x, algorithm="maxim

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mupad [B] time = 1.92, size = 19, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^{3\,{\mathrm {e}}^3}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {18}{9\,x+95}}} \end {gather*}

int(-(162*exp(exp(18/(9*x + 95)) - 1)*exp(3*exp(3))*exp(18/(9*x + 95)))/(1710*x + 81*x^2 + 9025),x)

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sympy [A] time = 0.40, size = 17, normalized size = 0.77 \begin {gather*} e^{e^{\frac {18}{9 x + 95}} - 1} e^{3 e^{3}} \end {gather*}

integrate(-162*exp(18/(9*x+95))*exp(3*exp(3))*exp(exp(18/(9*x+95))-1)/(81*x**2+1710*x+9025),x)

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3.30.60 \(\int -\frac {162 e^{-1+3 e^3+e^{\frac {18}{95+9 x}}+\frac {18}{95+9 x}}}{9025+1710 x+81 x^2} \, dx\)