How To Integrate 2^x? [Solved]

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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.

Explanation:

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

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

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