\(\int \frac {1}{625} (1633602+1623602 x+1623602 \log (4)) \, dx\) [7542]

Optimal result

Integrand size = 13, antiderivative size = 15 \[ \int \frac {1}{625} (1633602+1623602 x+1623602 \log (4)) \, dx=16 \left (x+\frac {811801 (1+x+\log (4))^2}{10000}\right ) \]

[Out]

16*x+3604/25*(2*ln(2)+x+1)*(901/50*ln(2)+901/100*x+901/100)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {9} \[ \int \frac {1}{625} (1633602+1623602 x+1623602 \log (4)) \, dx=\frac {(811801 x+816801+811801 \log (4))^2}{507375625} \]

[In]

Int[(1633602 + 1623602*x + 1623602*Log[4])/625,x]

[Out]

(816801 + 811801*x + 811801*Log[4])^2/507375625

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[a*((b + c*x)^2/(2*c)), x] /; FreeQ[{a, b, c}, x]

Rubi steps \begin{align*} \text {integral}& = \frac {(816801+811801 x+811801 \log (4))^2}{507375625} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.33 \[ \int \frac {1}{625} (1633602+1623602 x+1623602 \log (4)) \, dx=\frac {2}{625} \left (816801 x+\frac {811801 x^2}{2}+811801 x \log (4)\right ) \]

[In]

Integrate[(1633602 + 1623602*x + 1623602*Log[4])/625,x]

[Out]

(2*(816801*x + (811801*x^2)/2 + 811801*x*Log[4]))/625

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87

method	result	size
gosper	\(\frac {x \left (811801 x +3247204 \ln \left (2\right )+1633602\right )}{625}\)	\(13\)
default	\(\frac {3247204 x \ln \left (2\right )}{625}+\frac {811801 x^{2}}{625}+\frac {1633602 x}{625}\)	\(15\)
norman	\(\left (\frac {3247204 \ln \left (2\right )}{625}+\frac {1633602}{625}\right ) x +\frac {811801 x^{2}}{625}\)	\(15\)
risch	\(\frac {3247204 x \ln \left (2\right )}{625}+\frac {811801 x^{2}}{625}+\frac {1633602 x}{625}\)	\(15\)
parallelrisch	\(\left (\frac {3247204 \ln \left (2\right )}{625}+\frac {1633602}{625}\right ) x +\frac {811801 x^{2}}{625}\)	\(15\)
parts	\(\frac {3247204 x \ln \left (2\right )}{625}+\frac {811801 x^{2}}{625}+\frac {1633602 x}{625}\)	\(15\)

[In]

int(3247204/625*ln(2)+1623602/625*x+1633602/625,x,method=_RETURNVERBOSE)

[Out]

1/625*x*(811801*x+3247204*ln(2)+1633602)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {1}{625} (1633602+1623602 x+1623602 \log (4)) \, dx=\frac {811801}{625} \, x^{2} + \frac {3247204}{625} \, x \log \left (2\right ) + \frac {1633602}{625} \, x \]

[In]

integrate(3247204/625*log(2)+1623602/625*x+1633602/625,x, algorithm="fricas")

[Out]

811801/625*x^2 + 3247204/625*x*log(2) + 1633602/625*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.13 \[ \int \frac {1}{625} (1633602+1623602 x+1623602 \log (4)) \, dx=\frac {811801 x^{2}}{625} + x \left (\frac {1633602}{625} + \frac {3247204 \log {\left (2 \right )}}{625}\right ) \]

[In]

integrate(3247204/625*ln(2)+1623602/625*x+1633602/625,x)

[Out]

811801*x**2/625 + x*(1633602/625 + 3247204*log(2)/625)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {1}{625} (1633602+1623602 x+1623602 \log (4)) \, dx=\frac {811801}{625} \, x^{2} + \frac {3247204}{625} \, x \log \left (2\right ) + \frac {1633602}{625} \, x \]

[In]

integrate(3247204/625*log(2)+1623602/625*x+1633602/625,x, algorithm="maxima")

[Out]

811801/625*x^2 + 3247204/625*x*log(2) + 1633602/625*x

Giac [A] (verification not implemented)

none

Time = 0.32 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {1}{625} (1633602+1623602 x+1623602 \log (4)) \, dx=\frac {811801}{625} \, x^{2} + \frac {3247204}{625} \, x \log \left (2\right ) + \frac {1633602}{625} \, x \]

[In]

integrate(3247204/625*log(2)+1623602/625*x+1633602/625,x, algorithm="giac")

[Out]

811801/625*x^2 + 3247204/625*x*log(2) + 1633602/625*x

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {1}{625} (1633602+1623602 x+1623602 \log (4)) \, dx=\frac {811801\,x^2}{625}+\left (\frac {3247204\,\ln \left (2\right )}{625}+\frac {1633602}{625}\right )\,x \]

[In]

int((1623602*x)/625 + (3247204*log(2))/625 + 1633602/625,x)

[Out]

x*((3247204*log(2))/625 + 1633602/625) + (811801*x^2)/625