Intergration by Parts: int[x sec^2 x] dx

[flakine]

∫ x sec^2 x dx

udv=uv-∫vdu
u=x, du=dx, dv=sec^2 x dx, v=tan x

x sec^2 x dx= xtan x-∫tan x dx= xtan x-ln|secx|+C

Is this correct?

 

[skeeter]

Re: Intergration by Parts

take the derivative of your solution to confirm the result ... it's a good habit to get into.

 

[flakine]

It looks good to me. The text has a different answer.

xtan x + ln|cos x| =C

 

[galactus]

Same thing. Your answer is OK.