Integrand size = 58, antiderivative size = 28 \[ \int \frac {24 x^3+e^{\frac {-1296+576 x-9496 x^2+2256 x^3-19881 x^4}{144 x^2}} \left (432-96 x+376 x^3-6627 x^4\right )}{24 x^3} \, dx=e^{5-\left (\frac {1}{3}+\frac {3-x}{x}+\frac {47 x}{4}\right )^2}+x \]
[Out]
Time = 0.24 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.052, Rules used = {12, 14, 6838} \[ \int \frac {24 x^3+e^{\frac {-1296+576 x-9496 x^2+2256 x^3-19881 x^4}{144 x^2}} \left (432-96 x+376 x^3-6627 x^4\right )}{24 x^3} \, dx=e^{-\frac {19881 x^4-2256 x^3+9496 x^2-576 x+1296}{144 x^2}}+x \]
[In]
[Out]
Rule 12
Rule 14
Rule 6838
Rubi steps \begin{align*} \text {integral}& = \frac {1}{24} \int \frac {24 x^3+e^{\frac {-1296+576 x-9496 x^2+2256 x^3-19881 x^4}{144 x^2}} \left (432-96 x+376 x^3-6627 x^4\right )}{x^3} \, dx \\ & = \frac {1}{24} \int \left (24+\frac {e^{\frac {-1296+576 x-9496 x^2+2256 x^3-19881 x^4}{144 x^2}} \left (432-96 x+376 x^3-6627 x^4\right )}{x^3}\right ) \, dx \\ & = x+\frac {1}{24} \int \frac {e^{\frac {-1296+576 x-9496 x^2+2256 x^3-19881 x^4}{144 x^2}} \left (432-96 x+376 x^3-6627 x^4\right )}{x^3} \, dx \\ & = e^{-\frac {1296-576 x+9496 x^2-2256 x^3+19881 x^4}{144 x^2}}+x \\ \end{align*}
Time = 0.44 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {24 x^3+e^{\frac {-1296+576 x-9496 x^2+2256 x^3-19881 x^4}{144 x^2}} \left (432-96 x+376 x^3-6627 x^4\right )}{24 x^3} \, dx=e^{-\frac {1187}{18}-\frac {9}{x^2}+\frac {4}{x}+\frac {47 x}{3}-\frac {2209 x^2}{16}}+x \]
[In]
[Out]
Time = 0.41 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.04
method | result | size |
risch | \(x +{\mathrm e}^{-\frac {19881 x^{4}-2256 x^{3}+9496 x^{2}-576 x +1296}{144 x^{2}}}\) | \(29\) |
parallelrisch | \(x +{\mathrm e}^{-\frac {19881 x^{4}-2256 x^{3}+9496 x^{2}-576 x +1296}{144 x^{2}}}\) | \(29\) |
parts | \(x +{\mathrm e}^{\frac {-19881 x^{4}+2256 x^{3}-9496 x^{2}+576 x -1296}{144 x^{2}}}\) | \(29\) |
norman | \(\frac {x^{3}+x^{2} {\mathrm e}^{\frac {-19881 x^{4}+2256 x^{3}-9496 x^{2}+576 x -1296}{144 x^{2}}}}{x^{2}}\) | \(39\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {24 x^3+e^{\frac {-1296+576 x-9496 x^2+2256 x^3-19881 x^4}{144 x^2}} \left (432-96 x+376 x^3-6627 x^4\right )}{24 x^3} \, dx=x + e^{\left (-\frac {19881 \, x^{4} - 2256 \, x^{3} + 9496 \, x^{2} - 576 \, x + 1296}{144 \, x^{2}}\right )} \]
[In]
[Out]
Time = 0.11 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11 \[ \int \frac {24 x^3+e^{\frac {-1296+576 x-9496 x^2+2256 x^3-19881 x^4}{144 x^2}} \left (432-96 x+376 x^3-6627 x^4\right )}{24 x^3} \, dx=x + e^{\frac {- \frac {2209 x^{4}}{16} + \frac {47 x^{3}}{3} - \frac {1187 x^{2}}{18} + 4 x - 9}{x^{2}}} \]
[In]
[Out]
none
Time = 0.31 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.82 \[ \int \frac {24 x^3+e^{\frac {-1296+576 x-9496 x^2+2256 x^3-19881 x^4}{144 x^2}} \left (432-96 x+376 x^3-6627 x^4\right )}{24 x^3} \, dx=x + e^{\left (-\frac {2209}{16} \, x^{2} + \frac {47}{3} \, x + \frac {4}{x} - \frac {9}{x^{2}} - \frac {1187}{18}\right )} \]
[In]
[Out]
none
Time = 0.30 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {24 x^3+e^{\frac {-1296+576 x-9496 x^2+2256 x^3-19881 x^4}{144 x^2}} \left (432-96 x+376 x^3-6627 x^4\right )}{24 x^3} \, dx=x + e^{\left (-\frac {19881 \, x^{4} - 2256 \, x^{3} + 9496 \, x^{2} - 576 \, x + 1296}{144 \, x^{2}}\right )} \]
[In]
[Out]
Time = 12.98 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \frac {24 x^3+e^{\frac {-1296+576 x-9496 x^2+2256 x^3-19881 x^4}{144 x^2}} \left (432-96 x+376 x^3-6627 x^4\right )}{24 x^3} \, dx=x+\frac {{\mathrm {e}}^{-\frac {1187}{18}}\,{\mathrm {e}}^{4/x}\,{\mathrm {e}}^{-\frac {9}{x^2}}\,{\left ({\mathrm {e}}^x\right )}^{47/3}}{{\left ({\mathrm {e}}^{x^2}\right )}^{2209/16}} \]
[In]
[Out]