\(\int (-e^x+x^3+4 x^3 \log (x)) \, dx\) [5247]

Optimal result

Integrand size = 16, antiderivative size = 29 \[ \int \left (-e^x+x^3+4 x^3 \log (x)\right ) \, dx=-e^x+\left (-4+e^{\frac {3}{-5+e^{e^4}}}\right )^2+x^4 \log (x) \]

[Out]

(exp(3/(exp(exp(4))-5))-4)^2-exp(x)+x^4*ln(x)

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.41, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2225, 2341} \[ \int \left (-e^x+x^3+4 x^3 \log (x)\right ) \, dx=x^4 \log (x)-e^x \]

[In]

Int[-E^x + x^3 + 4*x^3*Log[x],x]

[Out]

-E^x + x^4*Log[x]

Rule 2225

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 2341

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Log[c*x^
n])/(d*(m + 1))), x] - Simp[b*n*((d*x)^(m + 1)/(d*(m + 1)^2)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rubi steps \begin{align*} \text {integral}& = \frac {x^4}{4}+4 \int x^3 \log (x) \, dx-\int e^x \, dx \\ & = -e^x+x^4 \log (x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.41 \[ \int \left (-e^x+x^3+4 x^3 \log (x)\right ) \, dx=-e^x+x^4 \log (x) \]

[In]

Integrate[-E^x + x^3 + 4*x^3*Log[x],x]

[Out]

-E^x + x^4*Log[x]

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.41

method	result	size
default	\(x^{4} \ln \left (x \right )-{\mathrm e}^{x}\)	\(12\)
norman	\(x^{4} \ln \left (x \right )-{\mathrm e}^{x}\)	\(12\)
risch	\(x^{4} \ln \left (x \right )-{\mathrm e}^{x}\)	\(12\)
parallelrisch	\(x^{4} \ln \left (x \right )-{\mathrm e}^{x}\)	\(12\)
parts	\(x^{4} \ln \left (x \right )-{\mathrm e}^{x}\)	\(12\)

[In]

int(4*x^3*ln(x)+x^3-exp(x),x,method=_RETURNVERBOSE)

[Out]

x^4*ln(x)-exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.38 \[ \int \left (-e^x+x^3+4 x^3 \log (x)\right ) \, dx=x^{4} \log \left (x\right ) - e^{x} \]

[In]

integrate(4*x^3*log(x)+x^3-exp(x),x, algorithm="fricas")

[Out]

x^4*log(x) - e^x

Sympy [A] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.28 \[ \int \left (-e^x+x^3+4 x^3 \log (x)\right ) \, dx=x^{4} \log {\left (x \right )} - e^{x} \]

[In]

integrate(4*x**3*ln(x)+x**3-exp(x),x)

[Out]

x**4*log(x) - exp(x)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.38 \[ \int \left (-e^x+x^3+4 x^3 \log (x)\right ) \, dx=x^{4} \log \left (x\right ) - e^{x} \]

[In]

integrate(4*x^3*log(x)+x^3-exp(x),x, algorithm="maxima")

[Out]

x^4*log(x) - e^x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.38 \[ \int \left (-e^x+x^3+4 x^3 \log (x)\right ) \, dx=x^{4} \log \left (x\right ) - e^{x} \]

[In]

integrate(4*x^3*log(x)+x^3-exp(x),x, algorithm="giac")

[Out]

x^4*log(x) - e^x

Mupad [B] (verification not implemented)

Time = 10.77 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.38 \[ \int \left (-e^x+x^3+4 x^3 \log (x)\right ) \, dx=x^4\,\ln \left (x\right )-{\mathrm {e}}^x \]

[In]

int(4*x^3*log(x) - exp(x) + x^3,x)

[Out]

x^4*log(x) - exp(x)