Optimal. Leaf size=20 \[ 3+e^{\frac {1}{25} \left (-16-\frac {7 x}{5}\right )^2}+3 x \]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 17, normalized size of antiderivative = 0.85, number of steps used = 4, number of rules used = 3, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.107, Rules used = {12, 2227, 2209} \begin {gather*} 3 x+e^{\frac {1}{625} (7 x+80)^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2209
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{625} \int \left (1875+e^{\frac {1}{625} \left (6400+1120 x+49 x^2\right )} (1120+98 x)\right ) \, dx\\ &=3 x+\frac {1}{625} \int e^{\frac {1}{625} \left (6400+1120 x+49 x^2\right )} (1120+98 x) \, dx\\ &=3 x+\frac {1}{625} \int e^{\frac {1}{625} (80+7 x)^2} (1120+98 x) \, dx\\ &=e^{\frac {1}{625} (80+7 x)^2}+3 x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 17, normalized size = 0.85 \begin {gather*} e^{\frac {1}{625} (80+7 x)^2}+3 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 15, normalized size = 0.75 \begin {gather*} 3 \, x + e^{\left (\frac {49}{625} \, x^{2} + \frac {224}{125} \, x + \frac {256}{25}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.18, size = 15, normalized size = 0.75 \begin {gather*} 3 \, x + e^{\left (\frac {49}{625} \, x^{2} + \frac {224}{125} \, x + \frac {256}{25}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 15, normalized size = 0.75
method | result | size |
risch | \(3 x +{\mathrm e}^{\frac {\left (7 x +80\right )^{2}}{625}}\) | \(15\) |
default | \(3 x +{\mathrm e}^{\frac {49}{625} x^{2}+\frac {224}{125} x +\frac {256}{25}}\) | \(16\) |
norman | \(3 x +{\mathrm e}^{\frac {49}{625} x^{2}+\frac {224}{125} x +\frac {256}{25}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.34, size = 15, normalized size = 0.75 \begin {gather*} 3 \, x + e^{\left (\frac {49}{625} \, x^{2} + \frac {224}{125} \, x + \frac {256}{25}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.51, size = 15, normalized size = 0.75 \begin {gather*} 3\,x+{\mathrm {e}}^{\frac {49\,x^2}{625}+\frac {224\,x}{125}+\frac {256}{25}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 19, normalized size = 0.95 \begin {gather*} 3 x + e^{\frac {49 x^{2}}{625} + \frac {224 x}{125} + \frac {256}{25}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________