Integrate and simplify the following function:

Question

y= ∫(ln√x/x^2)+x 2^(3-5x^2))dx

Answer 1

well,

∫ lnx/x^2 dx = -(lnx + 1)/x
recall that ln √x = 1/2 lnx

let u = 3-5x^2 and du=-10x dx
That gives you
∫ -1/10 2^u du
which is just 2^u / ln u

Now it's pretty straightforward