1.

Anti-derivative (Indefinate Integration) of e^(3x+2)

Answer»

Answer:

E^(3x+2)/3

Step-by-expllanation

u

=

3

x

+

2

 

⟶

 

d

u

d

x

=

3

(steps)  

⟶

 

d

x

=

1

3

d

u

:

=

1

3

∫

e

u

d

u

Now SOLVING:

∫

e

u

d

u

Apply exponential rule:

∫

a

u

d

u

=

a

u

ln

(

a

)

with  

a

=

e

:

=

e

u

Plug in solved integrals:

1

3

∫

e

u

d

u

=

e

u

3

Undo SUBSTITUTION  

u

=

3

x

+

2

:

=

e

3

x

+

2

3

The PROBLEM is solved:

∫

e

3

x

+

2

d

x

=

e

3

x

+

2

3

+

C


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