integrating 2^t

\displaystyle 2^t=e^{\ln(2^t)}=e^{t \ln 2}

Reply 3

Original post by Mr M

\displaystyle 2^t=e^{\ln(2^t)}=e^{t \ln 2}

Is that equivalent to 2^t/ln2?

Reply 4

Original post by cera ess six

Is that equivalent to 2^t/ln2?

Once integrated yes (plus a constant of integration).

Reply 5

Indeterminate

Original post by cera ess six

Is that equivalent to 2^t/ln2?

\displaystyle \int e^{ax} \ dx = \frac{1}{a}e^{ax} + C

right?

Why? a is just a number!!!

(edited 11 years ago)

Reply 6

Original post by Mr M

Once integrated yes (plus a constant of integration).

Oh ok how do you integrate further? this was one of the methods which confused me completely when I saw it.

Reply 7

Original post by Indeterminate

\displaystyle \int e^{ax} \ dx = \frac{1}{a}e^{2x} + C

right?

Why? a is just a number!!!

I don't much like the look of this!

Reply 8

Original post by cera ess six

Oh ok how do you integrate further? this was one of the methods which confused me completely when I saw it.

If you don't know how to tackle

\int e^{kx} \, dx

then you need to make sure you are confident about the basics before trying to extend your understanding further.

Reply 9

Original post by Indeterminate

\displaystyle \int e^{ax} \ dx = \frac{1}{a}e^{2x} + C

right?

Why? a is just a number!!!

I dont understand that approach sorry

Reply 10

Original post by cera ess six

I dont understand that approach sorry

It is wrong so I'm not surprised you don't understand it.

Reply 11

Felix Felicis

Original post by Indeterminate

\displaystyle \int e^{ax} \ dx = \frac{1}{a}e^{ax} + C

right?

Why? a is just a number!!!

Suspect that was a typo :tongue:

Reply 12

Indeterminate

Original post by Mr M

It is wrong so I'm not surprised you don't understand it.

Original post by cera ess six

I dont understand that approach sorry

A typo. I thought I should give one example but then decided to generalise. I forgot to change the 2 to an a :tongue:

Reply 13

Original post by Indeterminate

A typo. I thought I should give one example but then decided to generalise. I forgot to change the 2 to an a :tongue:

I assumed it probably was.

Reply 14

Original post by Mr M

If you don't know how to tackle

\int e^{kx} \, dx

then you need to make sure you are confident about the basics before trying to extend your understanding further.

Im sure integrating e^ax = 1/a e^ax just dont how it fits in X_X

Reply 15

Indeterminate

I would write

Since

\dfrac{d}{dt}(2^t) = 2^t \ln 2

\displaystyle \int 2^t \ dt =...

Reply 16

joostan

Original post by cera ess six

Im sure integrating e^ax = 1/a e^ax just dont how it fits in X_X

Try differentiating the result and see what you get.

Spoiler

Reply 17