Optimal. Leaf size=19 \[ 5 \left (\left (e^x-x\right )^2+\frac {128}{625 x^2}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 33, normalized size of antiderivative = 1.74, number of steps used = 8, number of rules used = 4, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {12, 14, 2194, 2176} \begin {gather*} 5 x^2+\frac {128}{125 x^2}+10 e^x+5 e^{2 x}-10 e^x (x+1) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{125} \int \frac {-256+1250 e^{2 x} x^3+1250 x^4+e^x \left (-1250 x^3-1250 x^4\right )}{x^3} \, dx\\ &=\frac {1}{125} \int \left (1250 e^{2 x}-1250 e^x (1+x)+\frac {2 \left (-128+625 x^4\right )}{x^3}\right ) \, dx\\ &=\frac {2}{125} \int \frac {-128+625 x^4}{x^3} \, dx+10 \int e^{2 x} \, dx-10 \int e^x (1+x) \, dx\\ &=5 e^{2 x}-10 e^x (1+x)+\frac {2}{125} \int \left (-\frac {128}{x^3}+625 x\right ) \, dx+10 \int e^x \, dx\\ &=10 e^x+5 e^{2 x}+\frac {128}{125 x^2}+5 x^2-10 e^x (1+x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 26, normalized size = 1.37 \begin {gather*} 5 e^{2 x}+\frac {128}{125 x^2}-10 e^x x+5 x^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.42, size = 28, normalized size = 1.47 \begin {gather*} \frac {625 \, x^{4} - 1250 \, x^{3} e^{x} + 625 \, x^{2} e^{\left (2 \, x\right )} + 128}{125 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.50, size = 28, normalized size = 1.47 \begin {gather*} \frac {625 \, x^{4} - 1250 \, x^{3} e^{x} + 625 \, x^{2} e^{\left (2 \, x\right )} + 128}{125 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 23, normalized size = 1.21
method | result | size |
default | \(5 x^{2}+\frac {128}{125 x^{2}}+5 \,{\mathrm e}^{2 x}-10 \,{\mathrm e}^{x} x\) | \(23\) |
risch | \(5 x^{2}+\frac {128}{125 x^{2}}+5 \,{\mathrm e}^{2 x}-10 \,{\mathrm e}^{x} x\) | \(23\) |
norman | \(\frac {\frac {128}{125}+5 x^{4}-10 \,{\mathrm e}^{x} x^{3}+5 \,{\mathrm e}^{2 x} x^{2}}{x^{2}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.43, size = 28, normalized size = 1.47 \begin {gather*} 5 \, x^{2} - 10 \, {\left (x - 1\right )} e^{x} + \frac {128}{125 \, x^{2}} + 5 \, e^{\left (2 \, x\right )} - 10 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.82, size = 22, normalized size = 1.16 \begin {gather*} 5\,{\mathrm {e}}^{2\,x}-10\,x\,{\mathrm {e}}^x+\frac {128}{125\,x^2}+5\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 24, normalized size = 1.26 \begin {gather*} 5 x^{2} - 10 x e^{x} + 5 e^{2 x} + \frac {128}{125 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________