# Homework Help: Integrate e^x cos(x)dx, how to do this?

1. Sep 24, 2004

### hytuoc

Some one plz show me how to do this problem below
Integral of e^x cos(x) dx
how to I integrate that?
thanks

2. Sep 24, 2004

### Pyrrhus

Try Integration by parts

$$\int u dv = uv -\int v du$$

try using $$u = e^x$$ and $$dv = \cos (x) dx$$

Last edited: Sep 24, 2004
3. Sep 24, 2004

### Hurkyl

Staff Emeritus
Your book will have this example (or one nearly identical to it) perfored step by step.

4. Sep 24, 2004

### Phymath

$$u = e^x \ dv = cos(x) dx$$
$$du = e^x dx \ v = sin(x)$$

$$\int e^x cos(x) dx = e^x sin(x) - \int sin(x) e^x dx$$

$$u = e^x \ dv = sin(x) dx$$
$$du = e^x dx \ v = -cos(x) dx$$
$$\int e^x cos(x) dx = e^x sin(x) - (-e^x cos(x) + \int e^x cos(x) dx)$$
$$= e^x sin(x) + e^x cos(x) - \int e^x cos(x) dx$$
$$\int e^x cos(x) dx + \int e^x cos(x) = e^x (sin(x) + cos(x))$$
$$2 \int e^x cos(x) dx = e^x(sin(x) + cos(x))$$
$$\int e^x cos(x) dx = 1/2 e^x (sin(x) + cos(x))$$ there you go intergration by parts follow
$$u v - \int v du$$

Last edited: Sep 24, 2004
5. Sep 24, 2004

### hytuoc

thanks so much