I assume you mean e2x. I tried this at the Wolframalpha site (using the search term: "integrate e^(2*x)"; the site says it is e2x/2. This can be obtained by a simple substitution.
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The anti derivative of negative sine is cosine.
.0015x2
2.5x2 + any constant
We say function F is an anti derivative, or indefinite integral of f if F' = f. Also, if f has an anti-derivative and is integrable on interval [a, b], then the definite integral of f from a to b is equal to F(b) - F(a) Thirdly, Let F(x) be the definite integral of integrable function f from a to x for all x in [a, b] of f, then F is an anti-derivative of f on [a,b] The definition of indefinite integral as anti-derivative, and the relation of definite integral with anti-derivative, we can conclude that integration and differentiation can be considered as two opposite operations.
x (ln x + 1) + Constant