3.20.1 \(\int (5+2 x+3 x^2+4 x^3) \, dx\) [1901]

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

[Out]

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

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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^4+x^3+x^2+5 x \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} 5 x+x^2+x^3+x^4 \end {gather*}

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 = 0.01, size = 14, normalized size = 1.08

method	result	size
gosper	\(x^{4}+x^{3}+x^{2}+5 x\)	\(14\)
default	\(x^{4}+x^{3}+x^{2}+5 x\)	\(14\)
norman	\(x^{4}+x^{3}+x^{2}+5 x\)	\(14\)
risch	\(x^{4}+x^{3}+x^{2}+5 x\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.27, size = 13, normalized size = 1.00 \begin {gather*} x^{4} + x^{3} + x^{2} + 5 \, x \end {gather*}

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 = 0.90, size = 13, normalized size = 1.00 \begin {gather*} x^{4} + x^{3} + x^{2} + 5 \, x \end {gather*}

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 = 0.01, size = 12, normalized size = 0.92 \begin {gather*} x^{4} + x^{3} + x^{2} + 5 x \end {gather*}

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 = 1.75, size = 13, normalized size = 1.00 \begin {gather*} x^{4} + x^{3} + x^{2} + 5 \, x \end {gather*}

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

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Mupad [B]
time = 0.03, size = 13, normalized size = 1.00 \begin {gather*} x^4+x^3+x^2+5\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x + 3*x^2 + 4*x^3 + 5,x)

[Out]

5*x + x^2 + x^3 + x^4

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