1. ## Integrate this

Can someone help me out? I have been gone, and am trying to figure this out myself.
Just start me?... what u, du, v, and dv equal?

integrate 3(sin x)^-2 dx

and

integrate (x^4)(e^-x) dx

2. Hello, Morgan82!

Use a trig identity on the first one . . .

$\int 3(\sin x)^{-2} \,dx$

We have: . $\int\frac{3\,dx}{\sin^2\!x} \;=\;3\int\csc^2\!x\,dx \;=\;-3\cot x + C$

3. For the second part you will use integration by parts 4 times. Use $u = x^4$ $dv=e^{-x}dx$ for the first iteration.

4. What is the integral of e^-x?
Originally Posted by lvleph
For the second part you will use integration by parts 4 times. Use $u = x^4$ $dv=e^{-x}$ for the first iteration.

5. Originally Posted by Morgan82
What is the integral of e^-x?
You can use u-substitution for that; $\int \! e^{-x} \,dx = \int \! e^u \cdot \frac{du}{dx} dx$