3.65.100 \(\int (3+\log (2 x^2)) \, dx\)

Optimal. Leaf size=15 \[ 8+x+\log ^2(15)+x \log \left (2 x^2\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.67, number of steps used = 2, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2295} \begin {gather*} x \log \left (2 x^2\right )+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3 + Log[2*x^2],x]

[Out]

x + x*Log[2*x^2]

Rule 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.67 \begin {gather*} x+x \log \left (2 x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3 + Log[2*x^2],x]

[Out]

x + x*Log[2*x^2]

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fricas [A]  time = 0.62, size = 10, normalized size = 0.67 \begin {gather*} x \log \left (2 \, x^{2}\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*log(2*x^2) + x

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giac [A]  time = 0.13, size = 10, normalized size = 0.67 \begin {gather*} x \log \left (2 \, x^{2}\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*log(2*x^2) + x

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maple [A]  time = 0.03, size = 11, normalized size = 0.73

method	result	size
norman	\(x +x \ln \left (2 x^{2}\right )\)	\(11\)
risch	\(x +x \ln \left (2 x^{2}\right )\)	\(11\)
default	\(x +x \ln \relax (2)+x \ln \left (x^{2}\right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.37, size = 10, normalized size = 0.67 \begin {gather*} x \log \left (2 \, x^{2}\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*log(2*x^2) + x

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mupad [B]  time = 4.04, size = 10, normalized size = 0.67 \begin {gather*} x\,\left (\ln \left (2\,x^2\right )+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(2*x^2) + 3,x)

[Out]

x*(log(2*x^2) + 1)

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sympy [A]  time = 0.08, size = 8, normalized size = 0.53 \begin {gather*} x \log {\left (2 x^{2} \right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*log(2*x**2) + x

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