3.104.14 \(\int (-e^{21}+e^{4+x} (-15-15 x)+60 x-e^{21} \log (x)) \, dx\)

Optimal. Leaf size=23 \[ x \left (15 \left (-e^{4+x}+2 x\right )-e^{21} \log (x)\right ) \]

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Rubi [A]  time = 0.02, antiderivative size = 31, normalized size of antiderivative = 1.35, number of steps used = 4, number of rules used = 3, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2176, 2194, 2295} \begin {gather*} 30 x^2+15 e^{x+4}-15 e^{x+4} (x+1)-e^{21} x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-E^21 + E^(4 + x)*(-15 - 15*x) + 60*x - E^21*Log[x],x]

[Out]

15*E^(4 + x) + 30*x^2 - 15*E^(4 + x)*(1 + x) - E^21*x*Log[x]

Rule 2176

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[((c + d*x)^m
*(b*F^(g*(e + f*x)))^n)/(f*g*n*Log[F]), x] - Dist[(d*m)/(f*g*n*Log[F]), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !$UseGamma === True

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]

Rule 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-e^{21} x+30 x^2-e^{21} \int \log (x) \, dx+\int e^{4+x} (-15-15 x) \, dx\\ &=30 x^2-15 e^{4+x} (1+x)-e^{21} x \log (x)+15 \int e^{4+x} \, dx\\ &=15 e^{4+x}+30 x^2-15 e^{4+x} (1+x)-e^{21} x \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 22, normalized size = 0.96 \begin {gather*} -15 e^{4+x} x+30 x^2-e^{21} x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-E^21 + E^(4 + x)*(-15 - 15*x) + 60*x - E^21*Log[x],x]

[Out]

-15*E^(4 + x)*x + 30*x^2 - E^21*x*Log[x]

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fricas [A]  time = 0.71, size = 20, normalized size = 0.87 \begin {gather*} -x e^{21} \log \relax (x) + 30 \, x^{2} - 15 \, x e^{\left (x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(21)*log(x)+(-15*x-15)*exp(4+x)-exp(21)+60*x,x, algorithm="fricas")

[Out]

-x*e^21*log(x) + 30*x^2 - 15*x*e^(x + 4)

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giac [A]  time = 0.15, size = 30, normalized size = 1.30 \begin {gather*} 30 \, x^{2} - {\left (x \log \relax (x) - x\right )} e^{21} - x e^{21} - 15 \, x e^{\left (x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(21)*log(x)+(-15*x-15)*exp(4+x)-exp(21)+60*x,x, algorithm="giac")

[Out]

30*x^2 - (x*log(x) - x)*e^21 - x*e^21 - 15*x*e^(x + 4)

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maple [A]  time = 0.03, size = 21, normalized size = 0.91

method	result	size
norman	\(30 x^{2}-15 x \,{\mathrm e}^{4+x}-\ln \relax (x ) {\mathrm e}^{21} x\)	\(21\)
risch	\(30 x^{2}-15 x \,{\mathrm e}^{4+x}-\ln \relax (x ) {\mathrm e}^{21} x\)	\(21\)
default	\(-15 \,{\mathrm e}^{4+x} \left (4+x \right )+60 \,{\mathrm e}^{4+x}+30 x^{2}-\ln \relax (x ) {\mathrm e}^{21} x\)	\(29\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(21)*ln(x)+(-15*x-15)*exp(4+x)-exp(21)+60*x,x,method=_RETURNVERBOSE)

[Out]

30*x^2-15*x*exp(4+x)-ln(x)*exp(21)*x

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maxima [A]  time = 0.34, size = 30, normalized size = 1.30 \begin {gather*} 30 \, x^{2} - {\left (x \log \relax (x) - x\right )} e^{21} - x e^{21} - 15 \, x e^{\left (x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(21)*log(x)+(-15*x-15)*exp(4+x)-exp(21)+60*x,x, algorithm="maxima")

[Out]

30*x^2 - (x*log(x) - x)*e^21 - x*e^21 - 15*x*e^(x + 4)

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mupad [B]  time = 9.30, size = 18, normalized size = 0.78 \begin {gather*} -x\,\left (15\,{\mathrm {e}}^{x+4}-30\,x+{\mathrm {e}}^{21}\,\ln \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(60*x - exp(21) - exp(21)*log(x) - exp(x + 4)*(15*x + 15),x)

[Out]

-x*(15*exp(x + 4) - 30*x + exp(21)*log(x))

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sympy [A]  time = 0.28, size = 20, normalized size = 0.87 \begin {gather*} 30 x^{2} - 15 x e^{x + 4} - x e^{21} \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(21)*ln(x)+(-15*x-15)*exp(4+x)-exp(21)+60*x,x)

[Out]

30*x**2 - 15*x*exp(x + 4) - x*exp(21)*log(x)

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