Homework Help: Computing antiderivatives (integration)

1. Jan 18, 2012

Nitrate

1. The problem statement, all variables and given/known data
integrate 4e^(2x)^(1/2) - 1/7e^(-pix)
using a guess and check method (haven't learned many rules of integration)

2. Relevant equations

3. The attempt at a solution
i'm not really sure how to do this integral... i tried
4/(2x)^(1/2)[e^(2x)^(1/2)] using a table of antiderivatives for the first part
but when i differentiated it, it did not give me the original function
i haven't tried the second bit yet.

2. Jan 18, 2012

The1337gamer

For the second term, do you know how to differentiate exponential functions?

Can you answer these questions, differentiate with respect to x:

e^x
18e^x
4e^2x
e^(x^2)
e^(x^(1/3))
e^(8x^(-2/3))

For the first term you need to use a substitution, try substituting u=x^1/2

3. Jan 18, 2012

HallsofIvy

If you have $\int f'(x)e^{f(x)}dx$ you could make the substitution $$u= f(x)$$ so that $$du= f'(x)dx$$ and the integral becomes $$\int e^u du= e^u+ C= e^{f(x)}+ C$$

HOWEVER, if that f'(x) is not in the integral originally (and is not a constant), you cannot put it in! Here, I don't believe that $$\int e^{(4x)^{1/2}}dx$$ can be integrated in terms of elementary functions.