3.28.13 \(\int (-8 x+e^{16+x+x^4} (1+4 x^3)) \, dx\)

Optimal. Leaf size=18 \[ -2+e^5+e^{16+x+x^4}-4 x^2 \]

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Rubi [A]  time = 0.03, antiderivative size = 14, normalized size of antiderivative = 0.78, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {6706} \begin {gather*} e^{x^4+x+16}-4 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-8*x + E^(16 + x + x^4)*(1 + 4*x^3),x]

[Out]

E^(16 + x + x^4) - 4*x^2

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-4 x^2+\int e^{16+x+x^4} \left (1+4 x^3\right ) \, dx\\ &=e^{16+x+x^4}-4 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 14, normalized size = 0.78 \begin {gather*} e^{16+x+x^4}-4 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-8*x + E^(16 + x + x^4)*(1 + 4*x^3),x]

[Out]

E^(16 + x + x^4) - 4*x^2

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fricas [A]  time = 0.71, size = 13, normalized size = 0.72 \begin {gather*} -4 \, x^{2} + e^{\left (x^{4} + x + 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3+1)*exp(x^4+x+16)-8*x,x, algorithm="fricas")

[Out]

-4*x^2 + e^(x^4 + x + 16)

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giac [A]  time = 0.23, size = 13, normalized size = 0.72 \begin {gather*} -4 \, x^{2} + e^{\left (x^{4} + x + 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3+1)*exp(x^4+x+16)-8*x,x, algorithm="giac")

[Out]

-4*x^2 + e^(x^4 + x + 16)

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maple [A]  time = 0.01, size = 14, normalized size = 0.78

method	result	size
default	\({\mathrm e}^{x^{4}+x +16}-4 x^{2}\)	\(14\)
norman	\({\mathrm e}^{x^{4}+x +16}-4 x^{2}\)	\(14\)
risch	\({\mathrm e}^{x^{4}+x +16}-4 x^{2}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x^3+1)*exp(x^4+x+16)-8*x,x,method=_RETURNVERBOSE)

[Out]

exp(x^4+x+16)-4*x^2

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maxima [A]  time = 0.51, size = 13, normalized size = 0.72 \begin {gather*} -4 \, x^{2} + e^{\left (x^{4} + x + 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3+1)*exp(x^4+x+16)-8*x,x, algorithm="maxima")

[Out]

-4*x^2 + e^(x^4 + x + 16)

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mupad [B]  time = 1.48, size = 15, normalized size = 0.83 \begin {gather*} {\mathrm {e}}^{x^4}\,{\mathrm {e}}^{16}\,{\mathrm {e}}^x-4\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x + x^4 + 16)*(4*x^3 + 1) - 8*x,x)

[Out]

exp(x^4)*exp(16)*exp(x) - 4*x^2

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sympy [A]  time = 0.09, size = 12, normalized size = 0.67 \begin {gather*} - 4 x^{2} + e^{x^{4} + x + 16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x**3+1)*exp(x**4+x+16)-8*x,x)

[Out]

-4*x**2 + exp(x**4 + x + 16)

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