3.x+x logx
The function is,
y = ∫ 1 x + x log x d x (1)
Let 1 + log x = r
Differentiate with respect to x ,
d r d x = 1 x d x = d r ⋅ x
Substitute the value of d x in equation (1) and use the formula of ∫ 1 x d x = log | x | + A , where E is constant.
∫ 1 x + x log x d x = ∫ 1 x ⋅ r ⋅ ( d r ⋅ x ) = ∫ 1 r d r = log | r | + D (2)
Where, D is constant.
Substitute the value of r in equation (2).
y = ( log | 1 + log x | ) + D
Thus, the value of integration is ( log | 1 + log x | ) + D .
The function is,
Let
Differentiate with respect to
Substitute the value of
Where,
Substitute the value of
Thus, the value of integration is
