Get the solution to "Determine the following indefinite integral. ∫ex+2dx"

High School
Calculus and Analysis
Calculus 2
Applications of integrals

aramutselv

Answered question

2021-12-26

Determine the following indefinite integral.

\int e^{x + 2} d x

Answer & Explanation

Esther Phillips

Beginner2021-12-27Added 34 answers

Step 1
Given integral is

\int e^{x + 2} d x

\int e^{x + 2} d x = \int e^{2} e^{x} d x

= e^{2} \int e^{x} d x

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

= e^{2 + x} + C

Step 2
Compute the derivative of the obtained integral.

{(e^{x + 2})}^{'} = e^{x + 2} {(x + 2)}^{'}

= e^{x + 2} (1)

= e^{x + 2}

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} d x

= \int e^{u} d u

Integral of exponential function:

\int a^{u} d u = \frac{a^{u}}{\ln (a)}

at a=e:

= e^{u}

Reverse replacement u=x+2:

= e^{x + 2}

Answer:

\int e^{x + 2} d x

= e^{x + 2} + C

Vasquez

Expert2022-01-07Added 669 answers

$\begin{matrix} G i v e n : \\ \int e^{x + 2} d x \\ \int e^{t} d t \\ e^{t} \\ S u b s t i t u t e b a c k \\ e^{x + 2} \\ A d d C \\ A n s w e r : \\ e^{x + 2} + C \end{matrix}$

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