Question

Integral ajuda

∫ te^t²

Answer 1

Temos o seguinte:

$\int {te^{t^2}} \, dt$

Assim:

$w =t^2 \therefore dw=2t \cdot dt \therefore dt= \dfrac{dw}{2t} \\ \\ \int {te^w} \, \frac{dw}{2t} = \frac{1}{2} \int {e^w} \, dw = \dfrac{e^w}{2} = \dfrac{e^{t^2}}{2} + C$

Logo:

$\int {te^{t^2}} \, dt = \dfrac{e^{t^2}}{2} + C$