Integrand size = 41, antiderivative size = 28 \[ \int \frac {3 e^{10 x^2}-30 x+12 x^2+18 x^3+60 e^{10 x^2} x^2 \log (x)}{x} \, dx=3 \left (4-(2+2 x) \left (5-x^2\right )+e^{10 x^2} \log (x)\right ) \]
[Out]
Time = 0.04 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89, number of steps used = 4, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {14, 2326} \[ \int \frac {3 e^{10 x^2}-30 x+12 x^2+18 x^3+60 e^{10 x^2} x^2 \log (x)}{x} \, dx=6 x^3+6 x^2+3 e^{10 x^2} \log (x)-30 x \]
[In]
[Out]
Rule 14
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \int \left (6 \left (-5+2 x+3 x^2\right )+\frac {3 e^{10 x^2} \left (1+20 x^2 \log (x)\right )}{x}\right ) \, dx \\ & = 3 \int \frac {e^{10 x^2} \left (1+20 x^2 \log (x)\right )}{x} \, dx+6 \int \left (-5+2 x+3 x^2\right ) \, dx \\ & = -30 x+6 x^2+6 x^3+3 e^{10 x^2} \log (x) \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {3 e^{10 x^2}-30 x+12 x^2+18 x^3+60 e^{10 x^2} x^2 \log (x)}{x} \, dx=3 \left (-10 x+2 x^2+2 x^3+e^{10 x^2} \log (x)\right ) \]
[In]
[Out]
Time = 0.13 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89
method | result | size |
risch | \(-30 x +3 \ln \left (x \right ) {\mathrm e}^{10 x^{2}}+6 x^{2}+6 x^{3}\) | \(25\) |
default | \(-30 x +3 \ln \left (x \right ) {\mathrm e}^{10 x^{2}}+6 x^{2}+6 x^{3}\) | \(27\) |
parallelrisch | \(-30 x +3 \ln \left (x \right ) {\mathrm e}^{10 x^{2}}+6 x^{2}+6 x^{3}\) | \(27\) |
parts | \(-30 x +3 \ln \left (x \right ) {\mathrm e}^{10 x^{2}}+6 x^{2}+6 x^{3}\) | \(27\) |
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86 \[ \int \frac {3 e^{10 x^2}-30 x+12 x^2+18 x^3+60 e^{10 x^2} x^2 \log (x)}{x} \, dx=6 \, x^{3} + 6 \, x^{2} + 3 \, e^{\left (10 \, x^{2}\right )} \log \left (x\right ) - 30 \, x \]
[In]
[Out]
Time = 0.10 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86 \[ \int \frac {3 e^{10 x^2}-30 x+12 x^2+18 x^3+60 e^{10 x^2} x^2 \log (x)}{x} \, dx=6 x^{3} + 6 x^{2} - 30 x + 3 e^{10 x^{2}} \log {\left (x \right )} \]
[In]
[Out]
none
Time = 0.22 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86 \[ \int \frac {3 e^{10 x^2}-30 x+12 x^2+18 x^3+60 e^{10 x^2} x^2 \log (x)}{x} \, dx=6 \, x^{3} + 6 \, x^{2} + 3 \, e^{\left (10 \, x^{2}\right )} \log \left (x\right ) - 30 \, x \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86 \[ \int \frac {3 e^{10 x^2}-30 x+12 x^2+18 x^3+60 e^{10 x^2} x^2 \log (x)}{x} \, dx=6 \, x^{3} + 6 \, x^{2} + 3 \, e^{\left (10 \, x^{2}\right )} \log \left (x\right ) - 30 \, x \]
[In]
[Out]
Time = 13.43 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.86 \[ \int \frac {3 e^{10 x^2}-30 x+12 x^2+18 x^3+60 e^{10 x^2} x^2 \log (x)}{x} \, dx=6\,x^2-30\,x+6\,x^3+3\,{\mathrm {e}}^{10\,x^2}\,\ln \left (x\right ) \]
[In]
[Out]