3.91.4 \(\int (1+4 x^3+5 x^4) \, dx\)

Optimal. Leaf size=15 \[ 2+e^3+x+x^3 \left (x+x^2\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.53, number of steps used = 1, number of rules used = 0, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^5+x^4+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + 4*x^3 + 5*x^4,x]

[Out]

x + x^4 + x^5

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x+x^4+x^5\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 0.53 \begin {gather*} x+x^4+x^5 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + 4*x^3 + 5*x^4,x]

[Out]

x + x^4 + x^5

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fricas [A]  time = 0.55, size = 8, normalized size = 0.53 \begin {gather*} x^{5} + x^{4} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x^4+4*x^3+1,x, algorithm="fricas")

[Out]

x^5 + x^4 + x

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giac [A]  time = 0.22, size = 8, normalized size = 0.53 \begin {gather*} x^{5} + x^{4} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x^4+4*x^3+1,x, algorithm="giac")

[Out]

x^5 + x^4 + x

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maple [A]  time = 0.01, size = 9, normalized size = 0.60

method	result	size
gosper	\(x^{5}+x^{4}+x\)	\(9\)
default	\(x^{5}+x^{4}+x\)	\(9\)
norman	\(x^{5}+x^{4}+x\)	\(9\)
risch	\(x^{5}+x^{4}+x\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5*x^4+4*x^3+1,x,method=_RETURNVERBOSE)

[Out]

x^5+x^4+x

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maxima [A]  time = 0.34, size = 8, normalized size = 0.53 \begin {gather*} x^{5} + x^{4} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x^4+4*x^3+1,x, algorithm="maxima")

[Out]

x^5 + x^4 + x

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mupad [B]  time = 0.02, size = 8, normalized size = 0.53 \begin {gather*} x^5+x^4+x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x^3 + 5*x^4 + 1,x)

[Out]

x + x^4 + x^5

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sympy [A]  time = 0.05, size = 7, normalized size = 0.47 \begin {gather*} x^{5} + x^{4} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(5*x**4+4*x**3+1,x)

[Out]

x**5 + x**4 + x

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