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Peyton Velez

Peyton Velez

Answered question

2022-06-07

How to solve: e x e 2 x + 3 d x
I tried substituting u = e x , d u = e x d x, and so I end up with:
1 u 2 + 3 d u
This looks like the derivative arctan ( x ), but I have a 3 instead of a 1. How can I solve this integral?

Answer & Explanation

Cristopher Barrera

Cristopher Barrera

Beginner2022-06-08Added 24 answers

Substitute u = 3 t.
1 u 2 + 3 d u = 1 3 1 t 2 + 1 d t = 1 3 arctan ( t ) = 1 3 arctan ( u 3 )
Done! Now put back u = e x to get the answer.
Mohammad Cannon

Mohammad Cannon

Beginner2022-06-09Added 4 answers

You can write:
1 u 2 + 3   d u = 1 3 ( u 2 3 + 1 )   d u = 1 3 1 ( u 3 ) 2 + 1   d u = 1 3 1 3 ( u 3 ) 2 + 1   d u = = 1 3 arctan ( u 3 ) + C
without using a substitution.

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