5. x log 2x
The integral is given as,
I = ∫ x log 2 x d x
Use integration by parts. Consider log 2 x as first function and x as second function.
I = ∫ x log 2 x d x = log 2 x ∫ x d x − ∫ ( d d x log 2 x ∫ x d x ) d x
On integrating, we get
I = log 2 x × x 2 2 − ∫ 2 2 x ( x 2 2 ) d x = x 2 log 2 x 2 − 1 2 ∫ x d x I = x 2 log 2 x 2 − x 2 4 + C
The integral is given as,
Use integration by parts. Consider
On integrating, we get
