3.10.82 \(\int (-20+10 \log (\frac {24}{x^2})) \, dx\) [982]

Optimal. Leaf size=9 \[ 10 x \log \left (\frac {24}{x^2}\right ) \]

[Out]

10*ln(24/x^2)*x

________________________________________________________________________________________

Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2332} \begin {gather*} 10 x \log \left (\frac {24}{x^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-20 + 10*Log[24/x^2],x]

[Out]

10*x*Log[24/x^2]

Rule 2332

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} &=-20 x+10 \int \log \left (\frac {24}{x^2}\right ) \, dx\\ &=10 x \log \left (\frac {24}{x^2}\right )\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} 10 x \log \left (\frac {24}{x^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-20 + 10*Log[24/x^2],x]

[Out]

10*x*Log[24/x^2]

________________________________________________________________________________________

Maple [A]
time = 0.17, size = 14, normalized size = 1.56

method	result	size
norman	\(10 \ln \left (\frac {24}{x^{2}}\right ) x\)	\(10\)
risch	\(10 \ln \left (\frac {24}{x^{2}}\right ) x\)	\(10\)
derivativedivides	\(10 \ln \left (24\right ) x +10 x \ln \left (\frac {1}{x^{2}}\right )\)	\(14\)
default	\(10 \ln \left (24\right ) x +10 x \ln \left (\frac {1}{x^{2}}\right )\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10*ln(24/x^2)-20,x,method=_RETURNVERBOSE)

[Out]

10*ln(24)*x+10*x*ln(1/x^2)

________________________________________________________________________________________

Maxima [A]
time = 0.34, size = 9, normalized size = 1.00 \begin {gather*} 10 \, x \log \left (\frac {24}{x^{2}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*log(24/x^2)-20,x, algorithm="maxima")

[Out]

10*x*log(24/x^2)

________________________________________________________________________________________

Fricas [A]
time = 0.40, size = 9, normalized size = 1.00 \begin {gather*} 10 \, x \log \left (\frac {24}{x^{2}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*log(24/x^2)-20,x, algorithm="fricas")

[Out]

10*x*log(24/x^2)

________________________________________________________________________________________

Sympy [A]
time = 0.03, size = 8, normalized size = 0.89 \begin {gather*} 10 x \log {\left (\frac {24}{x^{2}} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*ln(24/x**2)-20,x)

[Out]

10*x*log(24/x**2)

________________________________________________________________________________________

Giac [A]
time = 0.38, size = 9, normalized size = 1.00 \begin {gather*} 10 \, x \log \left (\frac {24}{x^{2}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*log(24/x^2)-20,x, algorithm="giac")

[Out]

10*x*log(24/x^2)

________________________________________________________________________________________

Mupad [B]
time = 0.66, size = 10, normalized size = 1.11 \begin {gather*} 10\,x\,\left (\ln \left (\frac {1}{x^2}\right )+\ln \left (24\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10*log(24/x^2) - 20,x)

[Out]

10*x*(log(1/x^2) + log(24))

________________________________________________________________________________________