Help plz.!! Given that $y=e^(x^2)$ , find $dy/dx$ Hence find $int xe^(x^2)dx$ ?

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Answer 1 · 2018-03-27T18:23:15

Use the chain rule to find $dy/dx$ .

$dy/dx =(2x)e^(x^2)$

As for the chain rule, let $u = x^2$ . Then $du = 2xdx$ and $dx = (du)/(2x)$ .

$I = 1/2int e^udu$

$I = 1/2e^u + C$

$I = 1/2e^(x^2) + C$

Alternatively we could have said

$I = 1/2int (2x)e^(x^2)dx$

$I = 1/2e^(x^2) + C$ (because integration is the opposite of differentiation)

This is the same answer we got using the substitution.

Hopefully this helps!

Help plz.!! Given that y=e^(x^2)y=e^(x^2), find dy/dxdy/dx Hence find int xe^(x^2)dxint xe^(x^2)dx?