3.92.95 \(\int \frac {400+\log (18)}{x^2} \, dx\)

Optimal. Leaf size=12 \[ 5+e-\frac {400+\log (18)}{x} \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.75, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \begin {gather*} -\frac {400+\log (18)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(400 + Log[18])/x^2,x]

[Out]

-((400 + Log[18])/x)

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=(400+\log (18)) \int \frac {1}{x^2} \, dx\\ &=-\frac {400+\log (18)}{x}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 9, normalized size = 0.75 \begin {gather*} -\frac {400+\log (18)}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(400 + Log[18])/x^2,x]

[Out]

-((400 + Log[18])/x)

________________________________________________________________________________________

fricas [A]  time = 0.87, size = 9, normalized size = 0.75 \begin {gather*} -\frac {\log \left (18\right ) + 400}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(18)+400)/x^2,x, algorithm="fricas")

[Out]

-(log(18) + 400)/x

________________________________________________________________________________________

giac [A]  time = 0.13, size = 9, normalized size = 0.75 \begin {gather*} -\frac {\log \left (18\right ) + 400}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(18)+400)/x^2,x, algorithm="giac")

[Out]

-(log(18) + 400)/x

________________________________________________________________________________________

maple [A]  time = 0.03, size = 10, normalized size = 0.83

method	result	size
gosper	\(-\frac {\ln \left (18\right )+400}{x}\)	\(10\)
default	\(-\frac {\ln \left (18\right )+400}{x}\)	\(10\)
norman	\(\frac {-\ln \left (18\right )-400}{x}\)	\(11\)
risch	\(-\frac {\ln \relax (2)}{x}-\frac {2 \ln \relax (3)}{x}-\frac {400}{x}\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((ln(18)+400)/x^2,x,method=_RETURNVERBOSE)

[Out]

-(ln(18)+400)/x

________________________________________________________________________________________

maxima [A]  time = 0.35, size = 9, normalized size = 0.75 \begin {gather*} -\frac {\log \left (18\right ) + 400}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(18)+400)/x^2,x, algorithm="maxima")

[Out]

-(log(18) + 400)/x

________________________________________________________________________________________

mupad [B]  time = 8.04, size = 9, normalized size = 0.75 \begin {gather*} -\frac {\ln \left (18\right )+400}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(18) + 400)/x^2,x)

[Out]

-(log(18) + 400)/x

________________________________________________________________________________________

sympy [A]  time = 0.05, size = 7, normalized size = 0.58 \begin {gather*} - \frac {\log {\left (18 \right )} + 400}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((ln(18)+400)/x**2,x)

[Out]

-(log(18) + 400)/x

________________________________________________________________________________________