I need help to solve The

Adham Hashem

Adham Hashem

Answered question

2022-04-27

I need help to solve The partial fraction to solve this problem. I do know how he solved the partial fraction only but I know rest of the solution. 

Answer & Explanation

star233

star233

Skilled2023-04-30Added 403 answers

exx2+1dx
Let's begin by using integration by parts. Let u=12ex and dv=dxx2+1. Then du=12exdx and v=tan1(x). Using the formula for integration by parts, we have:
exx2+1dx=12extan1(x)12extan1(x)dx
Now we need to evaluate the second integral. We can do this by using integration by parts again. Let u=tan1(x) and dv=12exdx. Then du=1x2+1dx and v=12ex. Using the formula for integration by parts again, we get:
12extan1(x)dx=12extan1(x)12(x2+1)exdx
We can now substitute this back into our original integral to get:
exx2+1dx=12extan1(x)(12extan1(x)12exx2+1dx)
Simplifying, we get:
exx2+1dx=12(extan1(x)+C)
where C is the constant of integration.
Therefore, the solution is 12(extan1(x)+C).

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