Question

can you split it like this?

Answer 1

\[\int\limits_{}^{}\frac{ \cos \sqrt{x} (\sin \sqrt{x})^{3}}{ \sqrt{x} }\]

Answer 2

^ this, into:

Answer 3

\[\int\limits_{}^{}\frac{ \cos \sqrt{x} }{ \sqrt{x}}\int\limits_{}^{}\frac{ (\sin \sqrt{x})^{3} }{ \sqrt{x} }\]

Answer 4

or just in addition?

Answer 5

you cant split a product like that

Answer 6

We can not do that for integrals as you have a product of 2 functions
you have to apply the u substitution

Answer 7

\[\int f(x)\times g(x) dx \ne \int f(x)dx \times \int g(x) dx \]

Answer 8

Yeah, i know about the u substitution. I was just wondering if i can do it this way. Thanks all!

Answer 9

for simple integrals we can not split it in the way you did
what we can do is to use u substitution and se what we get
the idea is to get an easier expression. So, as the sine is raise to the power of 3
it would be a good idea to substitute sine

Answer 10

Yw :^)