Integral of sin(lnx) + (lnx)^3/2 w.r.t. x

[sapiental]

g(x) = integral 0 to lnx (sin(t)+t^3/2))dt

find d/dx g(x):

let u = lnx


= sin(u) + u^3/2 du/dx
= sin(lnx)(1/x) + x^3/2(1/x)

Thanks

 

[HallsofIvy]

What is your question?

 

[drpizza]

I believe what you need to examine is the fundamental theorem of calculus, part 2. Check your text.

edit: in that section, you'll probably see some examples where they find the derivative of the integral of some function...