3.15.27 \(\int (7+240 e^{3 x}+192 e^{6 x}) \, dx\)

Optimal. Leaf size=20 \[ x+2 \left (5+\left (5+4 e^{3 x}\right )^2+3 x\right ) \]

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.90, number of steps used = 3, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {2194} \begin {gather*} 7 x+80 e^{3 x}+32 e^{6 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[7 + 240*E^(3*x) + 192*E^(6*x),x]

[Out]

80*E^(3*x) + 32*E^(6*x) + 7*x

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 {gather*} \begin {aligned} \text {integral} &=7 x+192 \int e^{6 x} \, dx+240 \int e^{3 x} \, dx\\ &=80 e^{3 x}+32 e^{6 x}+7 x\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 18, normalized size = 0.90 \begin {gather*} 80 e^{3 x}+32 e^{6 x}+7 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[7 + 240*E^(3*x) + 192*E^(6*x),x]

[Out]

80*E^(3*x) + 32*E^(6*x) + 7*x

________________________________________________________________________________________

fricas [A]  time = 0.71, size = 16, normalized size = 0.80 \begin {gather*} 7 \, x + 32 \, e^{\left (6 \, x\right )} + 80 \, e^{\left (3 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(192*exp(3*x)^2+240*exp(3*x)+7,x, algorithm="fricas")

[Out]

7*x + 32*e^(6*x) + 80*e^(3*x)

________________________________________________________________________________________

giac [A]  time = 0.44, size = 16, normalized size = 0.80 \begin {gather*} 7 \, x + 32 \, e^{\left (6 \, x\right )} + 80 \, e^{\left (3 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(192*exp(3*x)^2+240*exp(3*x)+7,x, algorithm="giac")

[Out]

7*x + 32*e^(6*x) + 80*e^(3*x)

________________________________________________________________________________________

maple [A]  time = 0.03, size = 17, normalized size = 0.85

method	result	size
risch	\(7 x +32 \,{\mathrm e}^{6 x}+80 \,{\mathrm e}^{3 x}\)	\(17\)
default	\(7 x +32 \,{\mathrm e}^{6 x}+80 \,{\mathrm e}^{3 x}\)	\(19\)
norman	\(7 x +32 \,{\mathrm e}^{6 x}+80 \,{\mathrm e}^{3 x}\)	\(19\)
derivativedivides	\(32 \,{\mathrm e}^{6 x}+80 \,{\mathrm e}^{3 x}+\frac {7 \ln \left ({\mathrm e}^{3 x}\right )}{3}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(192*exp(3*x)^2+240*exp(3*x)+7,x,method=_RETURNVERBOSE)

[Out]

7*x+32*exp(6*x)+80*exp(3*x)

________________________________________________________________________________________

maxima [A]  time = 0.44, size = 16, normalized size = 0.80 \begin {gather*} 7 \, x + 32 \, e^{\left (6 \, x\right )} + 80 \, e^{\left (3 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(192*exp(3*x)^2+240*exp(3*x)+7,x, algorithm="maxima")

[Out]

7*x + 32*e^(6*x) + 80*e^(3*x)

________________________________________________________________________________________

mupad [B]  time = 0.05, size = 16, normalized size = 0.80 \begin {gather*} 7\,x+80\,{\mathrm {e}}^{3\,x}+32\,{\mathrm {e}}^{6\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(240*exp(3*x) + 192*exp(6*x) + 7,x)

[Out]

7*x + 80*exp(3*x) + 32*exp(6*x)

________________________________________________________________________________________

sympy [A]  time = 0.08, size = 15, normalized size = 0.75 \begin {gather*} 7 x + 32 e^{6 x} + 80 e^{3 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(192*exp(3*x)**2+240*exp(3*x)+7,x)

[Out]

7*x + 32*exp(6*x) + 80*exp(3*x)

________________________________________________________________________________________