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1.

integral of [square root of( e^t-3)dt]

Sorry i didn't know how to do the square roots symbol and the integral symbol. Anyways, I tried to set e^t-3 as u and then got dt=du/e^t. Then I plugged in dt and couldn't go on after that.

2. integral of x^2[e^(x^3)]dx

so uh.... u substitution? but then what?

Ok basically, i think i don't know what your supposed do when u need to do a u-sub with e^something. Your help would be most appreciated.