3.47.39 \(\int (-1-\log (x^2)) \, dx\)

Optimal. Leaf size=15 \[ 3-e^5+x-x \log \left (x^2\right ) \]

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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 = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2295} \begin {gather*} x-x \log \left (x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 - Log[x^2],x]

[Out]

x - x*Log[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} &=-x-\int \log \left (x^2\right ) \, dx\\ &=x-x \log \left (x^2\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.60 \begin {gather*} x-x \log \left (x^2\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 - Log[x^2],x]

[Out]

x - x*Log[x^2]

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fricas [A]  time = 0.54, size = 9, normalized size = 0.60 \begin {gather*} -x \log \left (x^{2}\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1-log(x^2),x, algorithm="fricas")

[Out]

-x*log(x^2) + x

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giac [A]  time = 0.14, size = 9, normalized size = 0.60 \begin {gather*} -x \log \left (x^{2}\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1-log(x^2),x, algorithm="giac")

[Out]

-x*log(x^2) + x

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maple [A]  time = 0.01, size = 10, normalized size = 0.67

method	result	size
default	\(x -x \ln \left (x^{2}\right )\)	\(10\)
norman	\(x -x \ln \left (x^{2}\right )\)	\(10\)
risch	\(x -x \ln \left (x^{2}\right )\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1-ln(x^2),x,method=_RETURNVERBOSE)

[Out]

x-x*ln(x^2)

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maxima [A]  time = 0.36, size = 9, normalized size = 0.60 \begin {gather*} -x \log \left (x^{2}\right ) + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1-log(x^2),x, algorithm="maxima")

[Out]

-x*log(x^2) + x

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mupad [B]  time = 3.22, size = 9, normalized size = 0.60 \begin {gather*} -x\,\left (\ln \left (x^2\right )-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(- log(x^2) - 1,x)

[Out]

-x*(log(x^2) - 1)

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sympy [A]  time = 0.08, size = 7, normalized size = 0.47 \begin {gather*} - x \log {\left (x^{2} \right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1-ln(x**2),x)

[Out]

-x*log(x**2) + x

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