Integrand size = 19, antiderivative size = 14 \[ \int 4 e^{-3+3 x+25 x^2} (3+50 x) \, dx=4 e^{-3+3 x+25 x^2} \]
[Out]
Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 2268} \[ \int 4 e^{-3+3 x+25 x^2} (3+50 x) \, dx=4 e^{25 x^2+3 x-3} \]
[In]
[Out]
Rule 12
Rule 2268
Rubi steps \begin{align*} \text {integral}& = 4 \int e^{-3+3 x+25 x^2} (3+50 x) \, dx \\ & = 4 e^{-3+3 x+25 x^2} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int 4 e^{-3+3 x+25 x^2} (3+50 x) \, dx=4 e^{-3+3 x+25 x^2} \]
[In]
[Out]
Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00
method | result | size |
risch | \(4 \,{\mathrm e}^{25 x^{2}+3 x -3}\) | \(14\) |
gosper | \({\mathrm e}^{2 \ln \left (2\right )+25 x^{2}+3 x -3}\) | \(16\) |
derivativedivides | \({\mathrm e}^{2 \ln \left (2\right )+25 x^{2}+3 x -3}\) | \(16\) |
default | \({\mathrm e}^{2 \ln \left (2\right )+25 x^{2}+3 x -3}\) | \(16\) |
norman | \({\mathrm e}^{2 \ln \left (2\right )+25 x^{2}+3 x -3}\) | \(16\) |
parallelrisch | \({\mathrm e}^{2 \ln \left (2\right )+25 x^{2}+3 x -3}\) | \(16\) |
parts | \(-5 i \sqrt {\pi }\, {\mathrm e}^{2 \ln \left (2\right )-\frac {309}{100}} \operatorname {erf}\left (5 i x +\frac {3}{10} i\right ) x -\frac {3 i \sqrt {\pi }\, {\mathrm e}^{2 \ln \left (2\right )-\frac {309}{100}} \operatorname {erf}\left (5 i x +\frac {3}{10} i\right )}{10}+\frac {i {\mathrm e}^{2 \ln \left (2\right )-\frac {309}{100}} \left (50 x \,\operatorname {erf}\left (\frac {i \left (50 x +3\right )}{10}\right ) \sqrt {\pi }+3 \,\operatorname {erf}\left (\frac {i \left (50 x +3\right )}{10}\right ) \sqrt {\pi }-10 i {\mathrm e}^{\frac {\left (50 x +3\right )^{2}}{100}}\right )}{10}\) | \(98\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int 4 e^{-3+3 x+25 x^2} (3+50 x) \, dx=e^{\left (25 \, x^{2} + 3 \, x + 2 \, \log \left (2\right ) - 3\right )} \]
[In]
[Out]
Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int 4 e^{-3+3 x+25 x^2} (3+50 x) \, dx=4 e^{25 x^{2} + 3 x - 3} \]
[In]
[Out]
none
Time = 0.17 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93 \[ \int 4 e^{-3+3 x+25 x^2} (3+50 x) \, dx=4 \, e^{\left (25 \, x^{2} + 3 \, x - 3\right )} \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int 4 e^{-3+3 x+25 x^2} (3+50 x) \, dx=e^{\left (25 \, x^{2} + 3 \, x + 2 \, \log \left (2\right ) - 3\right )} \]
[In]
[Out]
Time = 8.31 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int 4 e^{-3+3 x+25 x^2} (3+50 x) \, dx=4\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{-3}\,{\mathrm {e}}^{25\,x^2} \]
[In]
[Out]