# How to integrate 2^{x}?

Integration is the inverse process of differentiation.

## Answer: The final value of the integration of 2^{x} is equal to 2^{x}/ln2 + c.

Go through the step-by-step solution to understand the explanation completely.

**Explanation:**

To find: ∫ 2^{x}dx

We may make use of the log property, which states:

e^{ln2} = 2

∫ 2^{x}dx = ∫ (e^{ln2})^{x}dx

∫ 2^{x}dx = ∫ (e^{xln2})dx ------(1)

let u = xln2,

⇒ du/dx = ln2

⇒ dx = du/ln2 -----(2)

Using the value obtained from equation (2) in equation (1), we get:

∫ (e^{xln2})dx = ∫ e^{u}×du/ln2

∫ (e^{xln2})dx = 1/ln2 ∫ e^{u}du = 1/ln2 × e^{u} + c

Now putting back e^{u} = e^{xln2} = 2^{x} we get,

1/ln2 × e^{u} + c = 1/ln2 × e^{xln2} + c = 2^{x}/ln2 + c

### Thus, the final value of the integration of 2^{x} gives the answer as 2^{x}/ln2 + c.

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