Question

Integrate 2 to the power(x+2)dx​

Answer 1

Answer:

1. =3x+1 this is answer correct or not correct

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Answer 2

The correct answer to the question is  4× $\frac{2^{x} }{log(2)}$  + c.

To Find:

The integral of  $\int\limit {2^{x+2} } \, dx$ =?

Solution:

Here, the question is to calculate the value of the improper integral  $\int\limit {2^{x+2} } \, dx$.

Let, I =  $\int\limit {2^{x+2} } \, dx$

⇒ I = $\int\limits{2^{x}.2^{2} } \, dx$

⇒ I = $4\int\limits {2^{x} } \, dx$

Now, this is a standard form of integration;

i.e., $\int\limits{a^{x} } \, dx = \frac{a^{x} }{log(a)} + c$ ; where c is the constant of improper integration.

In the above expression, the value of a is 2.

i.e., $\int\limits{2^{x} } \, dx$ = $\frac{2^{x} }{log(2)}$ + c

∴ I = $4[\frac{2^{x} }{log(a)} ] + c$

where c is the constant of integration.

Therefore,  $\int\limit {2^{x+2} } \, dx$ =  $4[\frac{2^{x} }{log(a)} ] + c$ .

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