3.95.87 \(\int \frac {3+3 x+2 x^2}{x} \, dx\)

Optimal. Leaf size=13 \[ x^2+3 (-2+x+\log (2 x)) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.85, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {14} \begin {gather*} x^2+3 x+3 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3 + 3*x + 2*x^2)/x,x]

[Out]

3*x + x^2 + 3*Log[x]

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (3+\frac {3}{x}+2 x\right ) \, dx\\ &=3 x+x^2+3 \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.85 \begin {gather*} 3 x+x^2+3 \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3 + 3*x + 2*x^2)/x,x]

[Out]

3*x + x^2 + 3*Log[x]

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fricas [A]  time = 0.87, size = 11, normalized size = 0.85 \begin {gather*} x^{2} + 3 \, x + 3 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2 + 3*x + 3*log(x)

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giac [A]  time = 0.13, size = 12, normalized size = 0.92 \begin {gather*} x^{2} + 3 \, x + 3 \, \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2 + 3*x + 3*log(abs(x))

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maple [A]  time = 0.02, size = 12, normalized size = 0.92

method	result	size
default	\(x^{2}+3 x +3 \ln \relax (x )\)	\(12\)
norman	\(x^{2}+3 x +3 \ln \relax (x )\)	\(12\)
risch	\(x^{2}+3 x +3 \ln \relax (x )\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2+3*x+3*ln(x)

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maxima [A]  time = 0.34, size = 11, normalized size = 0.85 \begin {gather*} x^{2} + 3 \, x + 3 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^2 + 3*x + 3*log(x)

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mupad [B]  time = 7.26, size = 11, normalized size = 0.85 \begin {gather*} 3\,x+3\,\ln \relax (x)+x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x + 2*x^2 + 3)/x,x)

[Out]

3*x + 3*log(x) + x^2

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sympy [A]  time = 0.06, size = 10, normalized size = 0.77 \begin {gather*} x^{2} + 3 x + 3 \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x**2 + 3*x + 3*log(x)

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