Calculate the indefinite integral:
∫(4x-3/x)dx
INT 4 dx - 3INTdx/x
4x-3lnx + Constant
Or you could have meant this (check parenthesis )
INT( 4x dx-3dx/x)=2x^3 -3lnx + C
To calculate the indefinite integral of ∫ (4x - 3/x) dx, we can use the method of integration by parts. The formula for integration by parts is:
∫ u dv = uv - ∫ v du
In this case, we can choose u = 4x and dv = (1 - 3/x) dx.
Now, let's calculate du and v:
du = d(4x) = 4 dx
v = ∫ (1 - 3/x) dx = ∫ dx - ∫ (3/x) dx = x - 3 ln|x|
We substitute these values into the formula for integration by parts:
∫ (4x - 3/x) dx = ∫ u dv
= uv - ∫ v du
= (4x)(x - 3 ln|x|) - ∫ (x - 3 ln|x|)(4 dx)
= 4x^2 - 12x ln|x| - ∫ 4x dx
= 4x^2 - 12x ln|x| - 2x^2 + C (constant of integration)
The final result of the indefinite integral is:
∫ (4x - 3/x) dx = 2x^2 - 12x ln|x| + C, where C is the constant of integration.