You really need to use trig. sub.? 'cause I'd put whereat and the integral is thus the original integral equals
If you let then . Substituting everything in leaves . After a bit of simplification, including changing to , you get . This simplifies to . From here, you can do a u-substitution, letting and . Plugging in gives . Integrating yields . Plugging back in for gives . Since , . Plugging back in, you get . If you draw out the triangle, you will see that if the tangent of an angle is , the sine of that angle is . Thus . Finally, plugging everything back into the original equation makes: . This simplifies to: or .
That problem was a huge pain to do with a trig sub, but it is right - I checked it on Maple.
I combined all the constants. Since you can pull a out of , just looking at the constants, you have . This simplifies to , which I pulled outside of the integral as a constant, leaving the integral . Turning into and multiplying the terms yields .
I hope that helped.