Integration by PartsFirst of all, why Integration by Parts?
As we know that
But what's the integration of
So, we use integration by parts technique for the integration of product of functions ( x and cosx in product form ).
Formula for Integration by PartsSuppose two functions u and v are in product form, then formula for finding their integration is
We can also remember the short formula for Integration by Parts which is usually without dx
|Example 1. Evaluate|
u = x u' = 1
|v = cosx|
|Example 2. Evaluate|
u = 2x2 u' = 4x
|v = sinx|
The later is again product of functions, and we have to use Integration by parts again. In the example above we have already found that, so using result from the above, we have
NOTE: 4c and c both are constants, so ignore 4.