\(\int \frac {400+\log (18)}{x^2} \, dx\) [9195]

Optimal result

Integrand size = 8, antiderivative size = 12 \[ \int \frac {400+\log (18)}{x^2} \, dx=5+e-\frac {400+\log (18)}{x} \]

[Out]

5-(ln(18)+400)/x+exp(1)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \[ \int \frac {400+\log (18)}{x^2} \, dx=-\frac {400+\log (18)}{x} \]

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {400+\log (18)}{x^2} \, dx=-\frac {400+\log (18)}{x} \]

[In]

Integrate[(400 + Log[18])/x^2,x]

[Out]

-((400 + Log[18])/x)

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83

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

[In]

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

[Out]

-(ln(18)+400)/x

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {400+\log (18)}{x^2} \, dx=-\frac {\log \left (18\right ) + 400}{x} \]

[In]

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

[Out]

-(log(18) + 400)/x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.58 \[ \int \frac {400+\log (18)}{x^2} \, dx=- \frac {\log {\left (18 \right )} + 400}{x} \]

[In]

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

[Out]

-(log(18) + 400)/x

Maxima [A] (verification not implemented)

none

Time = 0.17 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {400+\log (18)}{x^2} \, dx=-\frac {\log \left (18\right ) + 400}{x} \]

[In]

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

[Out]

-(log(18) + 400)/x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {400+\log (18)}{x^2} \, dx=-\frac {\log \left (18\right ) + 400}{x} \]

[In]

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

[Out]

-(log(18) + 400)/x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {400+\log (18)}{x^2} \, dx=-\frac {\ln \left (18\right )+400}{x} \]

[In]

int((log(18) + 400)/x^2,x)

[Out]

-(log(18) + 400)/x