Integrand size = 34, antiderivative size = 29 \[ \int \frac {64 x^3+e^2 \left (3+192 x^3-40 x^4+6 x^5\right )}{4 e^2} \, dx=\frac {1}{4} x \left (3+x^3 \left (x^2-4 \left (-4+2 \left (-4-\frac {2}{e^2}+x\right )\right )\right )\right ) \]
[Out]
Time = 0.01 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07, number of steps used = 3, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {12} \[ \int \frac {64 x^3+e^2 \left (3+192 x^3-40 x^4+6 x^5\right )}{4 e^2} \, dx=\frac {x^6}{4}-2 x^5+\frac {4 x^4}{e^2}+12 x^4+\frac {3 x}{4} \]
[In]
[Out]
Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {\int \left (64 x^3+e^2 \left (3+192 x^3-40 x^4+6 x^5\right )\right ) \, dx}{4 e^2} \\ & = \frac {4 x^4}{e^2}+\frac {1}{4} \int \left (3+192 x^3-40 x^4+6 x^5\right ) \, dx \\ & = \frac {3 x}{4}+12 x^4+\frac {4 x^4}{e^2}-2 x^5+\frac {x^6}{4} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.14 \[ \int \frac {64 x^3+e^2 \left (3+192 x^3-40 x^4+6 x^5\right )}{4 e^2} \, dx=\frac {3 x}{4}+\frac {4 \left (1+3 e^2\right ) x^4}{e^2}-2 x^5+\frac {x^6}{4} \]
[In]
[Out]
Time = 2.45 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93
method | result | size |
risch | \(\frac {x^{6}}{4}-2 x^{5}+12 x^{4}+4 \,{\mathrm e}^{-2} x^{4}+\frac {3 x}{4}\) | \(27\) |
norman | \(\frac {3 x}{4}-2 x^{5}+\frac {x^{6}}{4}+4 \left (3 \,{\mathrm e}^{2}+1\right ) {\mathrm e}^{-2} x^{4}\) | \(30\) |
gosper | \(\frac {x \left ({\mathrm e}^{2} x^{5}-8 x^{4} {\mathrm e}^{2}+48 x^{3} {\mathrm e}^{2}+16 x^{3}+3 \,{\mathrm e}^{2}\right ) {\mathrm e}^{-2}}{4}\) | \(38\) |
default | \(\frac {{\mathrm e}^{-2} \left (x^{6} {\mathrm e}^{2}-8 \,{\mathrm e}^{2} x^{5}+48 x^{4} {\mathrm e}^{2}+16 x^{4}+3 \,{\mathrm e}^{2} x \right )}{4}\) | \(38\) |
parallelrisch | \(\frac {{\mathrm e}^{-2} \left (x^{6} {\mathrm e}^{2}-8 \,{\mathrm e}^{2} x^{5}+48 x^{4} {\mathrm e}^{2}+16 x^{4}+3 \,{\mathrm e}^{2} x \right )}{4}\) | \(38\) |
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.03 \[ \int \frac {64 x^3+e^2 \left (3+192 x^3-40 x^4+6 x^5\right )}{4 e^2} \, dx=\frac {1}{4} \, {\left (16 \, x^{4} + {\left (x^{6} - 8 \, x^{5} + 48 \, x^{4} + 3 \, x\right )} e^{2}\right )} e^{\left (-2\right )} \]
[In]
[Out]
Time = 0.03 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.93 \[ \int \frac {64 x^3+e^2 \left (3+192 x^3-40 x^4+6 x^5\right )}{4 e^2} \, dx=\frac {x^{6}}{4} - 2 x^{5} + \frac {x^{4} \cdot \left (4 + 12 e^{2}\right )}{e^{2}} + \frac {3 x}{4} \]
[In]
[Out]
none
Time = 0.19 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.03 \[ \int \frac {64 x^3+e^2 \left (3+192 x^3-40 x^4+6 x^5\right )}{4 e^2} \, dx=\frac {1}{4} \, {\left (16 \, x^{4} + {\left (x^{6} - 8 \, x^{5} + 48 \, x^{4} + 3 \, x\right )} e^{2}\right )} e^{\left (-2\right )} \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.03 \[ \int \frac {64 x^3+e^2 \left (3+192 x^3-40 x^4+6 x^5\right )}{4 e^2} \, dx=\frac {1}{4} \, {\left (16 \, x^{4} + {\left (x^{6} - 8 \, x^{5} + 48 \, x^{4} + 3 \, x\right )} e^{2}\right )} e^{\left (-2\right )} \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.83 \[ \int \frac {64 x^3+e^2 \left (3+192 x^3-40 x^4+6 x^5\right )}{4 e^2} \, dx=\frac {x^6}{4}-2\,x^5+\left (4\,{\mathrm {e}}^{-2}+12\right )\,x^4+\frac {3\,x}{4} \]
[In]
[Out]