# Integration by Parts

Hi all,

I am having problems with the integral:

$$\int e^{(ax)} cos(bx) dx$$

I have got to $$\frac{e^{ax} sin(bx)}{b} - \int \frac{a e^{ax} sin(bx)}{b} dx$$

After this I can only see myself going around in circles.

Any help would be appreciated.

Cheers,

The Bob (2004 ©)

## Answers and Replies

The Bob said:
$$\int e^{(ax)} cos(bx) dx$$

I have got to $$\frac{e^{ax} sin(bx)}{b} - \int \frac{a e^{ax} sin(bx)}{b} dx$$

The integrals should be:

$$\int e^{(ax)} cos(bx) dx$$

and

$$\frac{e^{ax} sin(bx)}{b} - \int \frac{a e^{ax} sin(bx)}{b} dx$$

LaTex doesn't seem to be editable anymore.

The Bob (2004 ©)

Office_Shredder
Staff Emeritus
Gold Member
2021 Award
Go again, taking the integral on the RHS Since you get a -cos(x), where you would normally have subtraction from your integration by parts you get addition, except the whole thing is negative anyway, so your new integral (which is a bunch of constants times eaxcos(bx) ) turns out negative. Add that to both sides, and multiply/divide by constants to isolate your original integral

Office_Shredder said:
Go again, taking the integral on the RHS Since you get a -cos(x), where you would normally have subtraction from your integration by parts you get addition, except the whole thing is negative anyway, so your new integral (which is a bunch of constants times eaxcos(bx) ) turns out negative. Add that to both sides, and multiply/divide by constants to isolate your original integral
Cheers Office_Shredder. Sorry for the late reply, I have been very busy recently.

Thanks so much again ,

The Bob (2004 ©)