3.14.91 \(\int \frac {1}{5} (1+15 x^2) \, dx\)

Optimal. Leaf size=15 \[ \frac {x}{5}+x^3-\frac {\log (3)}{5} \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.60, 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*} x^3+\frac {x}{5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1 + 15*x^2)/5,x]

[Out]

x/5 + x^3

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 (1+15 x^2\right ) \, dx\\ &=\frac {x}{5}+x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.60 \begin {gather*} \frac {x}{5}+x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 + 15*x^2)/5,x]

[Out]

x/5 + x^3

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fricas [A]  time = 0.58, size = 7, normalized size = 0.47 \begin {gather*} x^{3} + \frac {1}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2+1/5,x, algorithm="fricas")

[Out]

x^3 + 1/5*x

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giac [A]  time = 0.29, size = 7, normalized size = 0.47 \begin {gather*} x^{3} + \frac {1}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2+1/5,x, algorithm="giac")

[Out]

x^3 + 1/5*x

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maple [A]  time = 0.01, size = 8, normalized size = 0.53

method	result	size
default	\(x^{3}+\frac {1}{5} x\)	\(8\)
norman	\(x^{3}+\frac {1}{5} x\)	\(8\)
risch	\(x^{3}+\frac {1}{5} x\)	\(8\)
gosper	\(\frac {\left (5 x^{2}+1\right ) x}{5}\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2+1/5,x,method=_RETURNVERBOSE)

[Out]

x^3+1/5*x

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maxima [A]  time = 0.42, size = 7, normalized size = 0.47 \begin {gather*} x^{3} + \frac {1}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2+1/5,x, algorithm="maxima")

[Out]

x^3 + 1/5*x

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mupad [B]  time = 0.02, size = 7, normalized size = 0.47 \begin {gather*} x^3+\frac {x}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2 + 1/5,x)

[Out]

x/5 + x^3

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sympy [A]  time = 0.05, size = 5, normalized size = 0.33 \begin {gather*} x^{3} + \frac {x}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x**2+1/5,x)

[Out]

x**3 + x/5

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