Question

e to the power - 4 x​

Answer 1

Step-by-step explanation:

Explanation:

We will use the integration rule for

e

x

:

∫

e

u

d

u

=

e

u

+

C

So, for the given integral, let

u

=

4

x

. This implies that

d

u

=

4

d

x

.

∫

e

4

x

d

x

=

1

4

∫

e

4

x

⋅

4

d

x

=

1

4

∫

e

u

d

u

=

1

4

e

u

+

C

Since

u

=

4

x

:

1

4

e

u

+

C

=

1

4

e

4

x

+

C

We can differentiate this answer to check that we get

e

4

x

. Indeed, through the chain rule, the

1

4

we had to add gets "undone" by the

4

coming from the power of

4

x

via the ch