what will be the integration of e^(x^2) ? solution should be with taking care of 12^th standard student

2*X*e^(x^2)

The usual differentiation of e^x is e^x, this is the formula we'll use here.

As the term to be differentiated is e^(x^2)

On differentiating it would be e^(x^2) * (differentiation of x^2)

Differentiation of x^2 is 2x

So the answer is 2x*e^(x^2)

Edit: I'm sry I didn't see that.

Integration of E^(x^2) would be (e^(x^2))/2x

The same logic applies here the only difference is we divide the term rather than multiplying it.

Formula is integral of e^xis E^x

Integral of e^(x^2) would be (e^(x^2)) divided by (differentiation of x^2)