Difficult Integral!

Ok maybe not, but could someone walk me through the steps of integrating something like cos(x^2) ?

I know the derivative of something like this is found via chain rule... is there some analogue for integration that I can use here?

Question

Difficult Integral!

Ok maybe not, but could someone walk me through the steps of integrating something like cos(x^2) ? 

I know the derivative of something like this is found via chain rule... is there some analogue for integration that I can use here?

amistre64 · Answer

just becasue we CAN integrate, does not mean that we can always integrate

amistre64 · Answer

there are tricks that can be had for cos(x^2) that have to do with maths like the Gamma function and/or power series

amistre64 · Answer

$$cos(u)=1-\frac{u^2}{2!}+\frac{u^4}{4!}-\frac{u^6}{6!}+...$$

anonymous · Answer

Yea, unless you're a college senior level math major or a grad student, you won't be asked to integrate things like cos(x^2).

amistre64 · Answer

$$\int\sum_{n=0}^{inf}\frac{1}{(2n)!}x^{4n}dx$$
might work out like this :)
$$\sum_{n=1}^{inf}\frac{1}{(2n)!~(4n+1)}x^{(4n+1)}$$