Question

XE power 4 power of X is 4 ​

Answer 1

Answer:

................

.....

Step-by-step explanation:

...........

Answer 2

Answer:

Remember that the formula that allows you to integrate a function by parts looks like this

∫

(

u

⋅

d

v

)

=

u

⋅

v

−

∫

(

v

⋅

d

u

)

, where

u

,

v

- are two functions of

x

;

d

u

,

d

v

- their derivatives.

So, you need to identify

u

and

d

v

, then calculate

d

u

and

v

.

If you take

u

=

x

and

d

v

=

e

4

x

, you will have

u

=

x

⇒

d

u

=

d

x

and

d

v

=

e

4

x

⇒

v

=

∫

(

e

4

x

d

x

)

=

1

4

⋅

e

4

x

Your target integral will thus be

∫

(

x

⋅

e

4

x

d

x

)

=

x

⋅

1

4

⋅

e

4

x

−

∫

(

1

4

e

4

x

⋅

d

x

)

∫

(

x

⋅

e

4

x

d

x

)

=

1

4

⋅

x

⋅

e

4

x

−

1

4

⋅

1

4

⋅

e

4

x

+

c

∫

(

x

⋅

e

4

x

d

x

)

=

1

4

e

4

x

(

x

−

1

4

)

+

c

∫

(

x

⋅

e

4

x

d

x

)

=

1

16

⋅

e

4

x

⋅

(

4

x

−

1

)

+

c