3.1901 \(\int (5+2 x+3 x^2+4 x^3) \, dx\)

Optimal. Leaf size=13 \[ x^4+x^3+x^2+5 x \]

[Out]

5*x + x^2 + x^3 + x^4

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Rubi [A]  time = 0.0018286, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ x^4+x^3+x^2+5 x \]

Antiderivative was successfully verified.

[In]

Int[5 + 2*x + 3*x^2 + 4*x^3,x]

[Out]

5*x + x^2 + x^3 + x^4

Rubi steps

\begin{align*} \int \left (5+2 x+3 x^2+4 x^3\right ) \, dx &=5 x+x^2+x^3+x^4\\ \end{align*}

Mathematica [A]  time = 0.0000453, size = 13, normalized size = 1. \[ x^4+x^3+x^2+5 x \]

Antiderivative was successfully verified.

[In]

Integrate[5 + 2*x + 3*x^2 + 4*x^3,x]

[Out]

5*x + x^2 + x^3 + x^4

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Maple [A]  time = 0., size = 14, normalized size = 1.1 \begin{align*}{x}^{4}+{x}^{3}+{x}^{2}+5\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x^3+3*x^2+2*x+5,x)

[Out]

x^4+x^3+x^2+5*x

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Maxima [A]  time = 0.984751, size = 18, normalized size = 1.38 \begin{align*} x^{4} + x^{3} + x^{2} + 5 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^3+3*x^2+2*x+5,x, algorithm="maxima")

[Out]

x^4 + x^3 + x^2 + 5*x

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Fricas [A]  time = 1.68933, size = 31, normalized size = 2.38 \begin{align*} x^{4} + x^{3} + x^{2} + 5 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^3+3*x^2+2*x+5,x, algorithm="fricas")

[Out]

x^4 + x^3 + x^2 + 5*x

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Sympy [A]  time = 0.053149, size = 12, normalized size = 0.92 \begin{align*} x^{4} + x^{3} + x^{2} + 5 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x**3+3*x**2+2*x+5,x)

[Out]

x**4 + x**3 + x**2 + 5*x

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Giac [A]  time = 1.07394, size = 18, normalized size = 1.38 \begin{align*} x^{4} + x^{3} + x^{2} + 5 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*x^3+3*x^2+2*x+5,x, algorithm="giac")

[Out]

x^4 + x^3 + x^2 + 5*x