3.103.2 \(\int \frac {1}{5} (5+4 x^3) \, dx\)

Optimal. Leaf size=20 \[ -2-(-9+e)^2+e+x+\frac {1}{5} \left (-1+x^4\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.45, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {12} \begin {gather*} \frac {x^4}{5}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(5 + 4*x^3)/5,x]

[Out]

x + x^4/5

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (5+4 x^3\right ) \, dx\\ &=x+\frac {x^4}{5}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.45 \begin {gather*} x+\frac {x^4}{5} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(5 + 4*x^3)/5,x]

[Out]

x + x^4/5

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fricas [A]  time = 0.85, size = 7, normalized size = 0.35 \begin {gather*} \frac {1}{5} \, x^{4} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/5*x^4 + x

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giac [A]  time = 0.13, size = 7, normalized size = 0.35 \begin {gather*} \frac {1}{5} \, x^{4} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/5*x^4 + x

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maple [A]  time = 0.01, size = 8, normalized size = 0.40

method	result	size
default	\(\frac {1}{5} x^{4}+x\)	\(8\)
norman	\(\frac {1}{5} x^{4}+x\)	\(8\)
risch	\(\frac {1}{5} x^{4}+x\)	\(8\)
gosper	\(\frac {x \left (x^{3}+5\right )}{5}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/5*x^4+x

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maxima [A]  time = 0.35, size = 7, normalized size = 0.35 \begin {gather*} \frac {1}{5} \, x^{4} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/5*x^4 + x

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mupad [B]  time = 0.02, size = 7, normalized size = 0.35 \begin {gather*} \frac {x^4}{5}+x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x^3)/5 + 1,x)

[Out]

x + x^4/5

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sympy [A]  time = 0.05, size = 5, normalized size = 0.25 \begin {gather*} \frac {x^{4}}{5} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x**4/5 + x

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