How do I find the antiderivative of e^(2x) + 1?

1 Answer
Gió
Jan 27, 2015

I would use the idea of integral (indefinite) and the techniques connected with this procedure:
1) I can write:
inte^(2x)+1dx
2) I can use the fact the the integral of a sum is equal to the sum of the integrals, giving:
inte^(2x)dx+int1dx
3) I can use the fact that the integral of the exponential is equal to itself (but here we have to consider the exponent 2x as well) and that 1 can be written as x^0;
inte^(2x)dx+intx^0dx=
e^(2x)/2+x+c

I also evaluate the integral of x^0 using the fact that the integral of x^n is x^(n+1)/(n+1)

4) You can now check the result (the anti-derivative) obtained above deriving it to see if it gives the initial function e^(2x)+1.

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