3.2.9 \(\int (7+e^3-2 x-180 x^3+45 x^4) \, dx\)

Optimal. Leaf size=17 \[ (-5+x) \left (2+e^3-x+9 x^4\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.35, number of steps used = 1, number of rules used = 0, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 9 x^5-45 x^4-x^2+\left (7+e^3\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[7 + E^3 - 2*x - 180*x^3 + 45*x^4,x]

[Out]

(7 + E^3)*x - x^2 - 45*x^4 + 9*x^5

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\left (7+e^3\right ) x-x^2-45 x^4+9 x^5\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 24, normalized size = 1.41 \begin {gather*} 7 x+e^3 x-x^2-45 x^4+9 x^5 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[7 + E^3 - 2*x - 180*x^3 + 45*x^4,x]

[Out]

7*x + E^3*x - x^2 - 45*x^4 + 9*x^5

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fricas [A]  time = 0.48, size = 23, normalized size = 1.35 \begin {gather*} 9 \, x^{5} - 45 \, x^{4} - x^{2} + x e^{3} + 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(3)+45*x^4-180*x^3-2*x+7,x, algorithm="fricas")

[Out]

9*x^5 - 45*x^4 - x^2 + x*e^3 + 7*x

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giac [A]  time = 0.26, size = 23, normalized size = 1.35 \begin {gather*} 9 \, x^{5} - 45 \, x^{4} - x^{2} + x e^{3} + 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(3)+45*x^4-180*x^3-2*x+7,x, algorithm="giac")

[Out]

9*x^5 - 45*x^4 - x^2 + x*e^3 + 7*x

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maple [A]  time = 0.02, size = 23, normalized size = 1.35

method	result	size
norman	\(9 x^{5}-45 x^{4}-x^{2}+\left (7+{\mathrm e}^{3}\right ) x\)	\(23\)
gosper	\(9 x^{5}-45 x^{4}+x \,{\mathrm e}^{3}-x^{2}+7 x\)	\(24\)
default	\(9 x^{5}-45 x^{4}+x \,{\mathrm e}^{3}-x^{2}+7 x\)	\(24\)
risch	\(9 x^{5}-45 x^{4}+x \,{\mathrm e}^{3}-x^{2}+7 x\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(3)+45*x^4-180*x^3-2*x+7,x,method=_RETURNVERBOSE)

[Out]

9*x^5-45*x^4-x^2+(7+exp(3))*x

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maxima [A]  time = 0.42, size = 23, normalized size = 1.35 \begin {gather*} 9 \, x^{5} - 45 \, x^{4} - x^{2} + x e^{3} + 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(3)+45*x^4-180*x^3-2*x+7,x, algorithm="maxima")

[Out]

9*x^5 - 45*x^4 - x^2 + x*e^3 + 7*x

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mupad [B]  time = 0.04, size = 22, normalized size = 1.29 \begin {gather*} 9\,x^5-45\,x^4-x^2+\left ({\mathrm {e}}^3+7\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(3) - 2*x - 180*x^3 + 45*x^4 + 7,x)

[Out]

x*(exp(3) + 7) - x^2 - 45*x^4 + 9*x^5

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sympy [A]  time = 0.06, size = 19, normalized size = 1.12 \begin {gather*} 9 x^{5} - 45 x^{4} - x^{2} + x \left (7 + e^{3}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(3)+45*x**4-180*x**3-2*x+7,x)

[Out]

9*x**5 - 45*x**4 - x**2 + x*(7 + exp(3))

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