Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am trying to integrate the following:

$$\int e^{-2y}\cos(y^2) \, dy$$

I cannot identify a suitable substitution, and integration by parts would seem to go round in circles.

Please provide me with any minor hints in the right direction (homework).

share|improve this question
    
Are you sure you have the problem right? You may know that if $f(x)$ is a quadratic polynomial then there is no closed form for $\int e^{f(x)}\,dx$, and that's what your integral looks like. –  Gerry Myerson Oct 15 '12 at 0:39

2 Answers 2

up vote 1 down vote accepted

Is it given as indefinite integral as you wrote? If it is a definite (improper) integral given from $-\infty$ to $\infty$, I would try by writing $e^{iy^{2}} = \cos(y^{2}) + i\sin(y^{2})$. Convergence seems easy to show in this case.

I don't know if it is doable for indefinite integral.

share|improve this answer

Notice $\int{e^{-2y}cos(y^2)}dy = -1/2\int{cos(y^2)de^{-2y}}$. Now use Integration by parts. It is not suppose to go round on circles. Just Let $I = \int{e^{-2y}cos(y^2)}dy$, and then until you get the same expression back, you just solve for $I$.

share|improve this answer
    
The problem is that after using IBP twice, you get $\int y^2e^{-2y} \cos(y^2) $... –  N. S. Oct 15 '12 at 0:31

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.