Optimal. Leaf size=19 \[ \frac {1}{25} \left (7+e^{x^2}+x\right ) (4+4 x)^2 \]
[Out]
________________________________________________________________________________________
Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(51\) vs. \(2(19)=38\).
time = 0.05, antiderivative size = 51, normalized size of antiderivative = 2.68, number of steps
used = 10, number of rules used = 5, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 2258,
2235, 2240, 2243} \begin {gather*} \frac {16 x^3}{25}+\frac {16}{25} e^{x^2} x^2+\frac {144 x^2}{25}+\frac {32 e^{x^2} x}{25}+\frac {16 e^{x^2}}{25}+\frac {48 x}{5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2235
Rule 2240
Rule 2243
Rule 2258
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \left (240+288 x+48 x^2+e^{x^2} \left (32+64 x+64 x^2+32 x^3\right )\right ) \, dx\\ &=\frac {48 x}{5}+\frac {144 x^2}{25}+\frac {16 x^3}{25}+\frac {1}{25} \int e^{x^2} \left (32+64 x+64 x^2+32 x^3\right ) \, dx\\ &=\frac {48 x}{5}+\frac {144 x^2}{25}+\frac {16 x^3}{25}+\frac {1}{25} \int \left (32 e^{x^2}+64 e^{x^2} x+64 e^{x^2} x^2+32 e^{x^2} x^3\right ) \, dx\\ &=\frac {48 x}{5}+\frac {144 x^2}{25}+\frac {16 x^3}{25}+\frac {32}{25} \int e^{x^2} \, dx+\frac {32}{25} \int e^{x^2} x^3 \, dx+\frac {64}{25} \int e^{x^2} x \, dx+\frac {64}{25} \int e^{x^2} x^2 \, dx\\ &=\frac {32 e^{x^2}}{25}+\frac {48 x}{5}+\frac {32 e^{x^2} x}{25}+\frac {144 x^2}{25}+\frac {16}{25} e^{x^2} x^2+\frac {16 x^3}{25}+\frac {16}{25} \sqrt {\pi } \text {erfi}(x)-\frac {32}{25} \int e^{x^2} \, dx-\frac {32}{25} \int e^{x^2} x \, dx\\ &=\frac {16 e^{x^2}}{25}+\frac {48 x}{5}+\frac {32 e^{x^2} x}{25}+\frac {144 x^2}{25}+\frac {16}{25} e^{x^2} x^2+\frac {16 x^3}{25}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.13, size = 26, normalized size = 1.37 \begin {gather*} \frac {16}{25} \left (e^{x^2} (1+x)^2+x \left (15+9 x+x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(36\) vs.
\(2(16)=32\).
time = 0.07, size = 37, normalized size = 1.95
method | result | size |
risch | \(\frac {\left (16 x^{2}+32 x +16\right ) {\mathrm e}^{x^{2}}}{25}+\frac {16 x^{3}}{25}+\frac {144 x^{2}}{25}+\frac {48 x}{5}\) | \(31\) |
default | \(\frac {48 x}{5}+\frac {144 x^{2}}{25}+\frac {16 x^{3}}{25}+\frac {16 x^{2} {\mathrm e}^{x^{2}}}{25}+\frac {16 \,{\mathrm e}^{x^{2}}}{25}+\frac {32 \,{\mathrm e}^{x^{2}} x}{25}\) | \(37\) |
norman | \(\frac {48 x}{5}+\frac {144 x^{2}}{25}+\frac {16 x^{3}}{25}+\frac {16 x^{2} {\mathrm e}^{x^{2}}}{25}+\frac {16 \,{\mathrm e}^{x^{2}}}{25}+\frac {32 \,{\mathrm e}^{x^{2}} x}{25}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 28, normalized size = 1.47 \begin {gather*} \frac {16}{25} \, x^{3} + \frac {144}{25} \, x^{2} + \frac {16}{25} \, {\left (x^{2} + 2 \, x + 1\right )} e^{\left (x^{2}\right )} + \frac {48}{5} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.39, size = 28, normalized size = 1.47 \begin {gather*} \frac {16}{25} \, x^{3} + \frac {144}{25} \, x^{2} + \frac {16}{25} \, {\left (x^{2} + 2 \, x + 1\right )} e^{\left (x^{2}\right )} + \frac {48}{5} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 34, normalized size = 1.79 \begin {gather*} \frac {16 x^{3}}{25} + \frac {144 x^{2}}{25} + \frac {48 x}{5} + \frac {\left (16 x^{2} + 32 x + 16\right ) e^{x^{2}}}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.39, size = 28, normalized size = 1.47 \begin {gather*} \frac {16}{25} \, x^{3} + \frac {144}{25} \, x^{2} + \frac {16}{25} \, {\left (x^{2} + 2 \, x + 1\right )} e^{\left (x^{2}\right )} + \frac {48}{5} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.07, size = 36, normalized size = 1.89 \begin {gather*} \frac {48\,x}{5}+\frac {16\,{\mathrm {e}}^{x^2}}{25}+\frac {32\,x\,{\mathrm {e}}^{x^2}}{25}+\frac {16\,x^2\,{\mathrm {e}}^{x^2}}{25}+\frac {144\,x^2}{25}+\frac {16\,x^3}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________