How to integrate 2x?
Integration is the inverse process of differentiation.
Answer: The final value of the integration of 2x is equal to 2x/ln2 + c.
Go through the step-by-step solution to understand the explanation completely.
To find: ∫ 2xdx
We may make use of the log property, which states:
eln2 = 2
∫ 2xdx = ∫ (eln2)xdx
∫ 2xdx = ∫ (exln2)dx ------(1)
let u = xln2,
⇒ du/dx = ln2
⇒ dx = du/ln2 -----(2)
Using the value obtained from equation (2) in equation (1), we get:
∫ (exln2)dx = ∫ eu×du/ln2
∫ (exln2)dx = 1/ln2 ∫ eudu = 1/ln2 × eu + c
Now putting back eu = exln2 = 2x we get,
1/ln2 × eu + c = 1/ln2 × exln2 + c = 2x/ln2 + c