aramutselv

2021-12-26

Determine the following indefinite integral.

$\int {e}^{x+2}dx$

Esther Phillips

Beginner2021-12-27Added 34 answers

Step 1

Given integral is$\int {e}^{x+2}dx$ .

$\int {e}^{x+2}dx=\int {e}^{2}{e}^{x}dx$

$={e}^{2}\int {e}^{x}dx$

$={e}^{2}{e}^{x}+C$

$={e}^{2+x}+C$

Step 2

Compute the derivative of the obtained integral.

$\left({e}^{x+2}\right)}^{\prime}={e}^{x+2}{(x+2)}^{\prime$

$={e}^{x+2}\left(1\right)$

$={e}^{x+2}$

Hence, the derivative of the integral is the given function of the integrand.

Given integral is

Step 2

Compute the derivative of the obtained integral.

Hence, the derivative of the integral is the given function of the integrand.

Elaine Verrett

Beginner2021-12-28Added 41 answers

It is required to calculate:

$\int {e}^{x+2}dx$

$=\int {e}^{u}du$

Integral of exponential function:

$\int {a}^{u}du=\frac{{a}^{u}}{\mathrm{ln}\left(a\right)}$ at a=e:

$={e}^{u}$

Reverse replacement u=x+2:

$={e}^{x+2}$

Answer:

$\int {e}^{x+2}dx$

$={e}^{x+2}+C$

Integral of exponential function:

Reverse replacement u=x+2:

Answer:

Vasquez

Expert2022-01-07Added 669 answers

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