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

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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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