Wednesday, December 5, 2012

`int (x^2 + 2^(-x)) dx` Find the indefinite integral

Indefinite integral is additive, i.e. `int (f+g) = int f + int g.` Therefore


`int (x^2 + 2^(-x)) dx =int x^2 dx + int 2^(-x) dx.`


Both integrals are table ones or very close to them, so the answer is


`x^3/3 - 1/ln(2) 2^(-x) + C,`


where `C` is an arbitrary constant.

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