Integration

[Luna642]

What is the antiderivative of (4^x - 2^x + 1) / 2^x?

 

[pka]

What is the antiderivative of (4^x - 2^x + 1) / 2^x?

Write \(\dfrac{4^x-2^x+1}{2^x}\) as \(2^x-1+2^{-x}\).
Can you continue? Please post you own work.

 

[Steven G]

Are you integrating wrt x, y , t ....?

 

[Deleted member 4993]

What is the antiderivative of (4^x - 2^x + 1) / 2^x?

Do you know the anti-derivative of:

2^x.............................. w.r.t. x?

Do you know the derivative of: .......................................................added later

2^x.............................. w.r.t. x?

 

[Steven G]

Let's see.

y=a^x.

ln(y) = xln(a)

(1/y)y' = ln(a)

Then y' = yln(a)

So y' = a^xln(a)

Does that help?