What is the integral of (e^{2x}+1)/(e^{2x)} ?

The integral of (e^{2x}+1)/(e^{2x)} is -1/2 e^{-2x}(e^{2x}+1)+x+C

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integral of (e^{2x}+1)/(e^{2x)}

\int \frac{e ^{2 x} + 1}{e ^{2 x}} d x

- \frac{1}{2} e^{- 2 x} (e^{2 x} + 1) + x + C

Solution steps

\int \frac{e ^{2 x} + 1}{e ^{2 x}} d x

Apply Integration By Parts

: - \frac{1}{2} e^{- 2 x} (e^{2 x} + 1) - \int - 1 d x

= - \frac{1}{2} e^{- 2 x} (e^{2 x} + 1) - \int - 1 d x

\int - 1 d x = - x

= - \frac{1}{2} e^{- 2 x} (e^{2 x} + 1) - (- x)

Simplify

= - \frac{1}{2} e^{- 2 x} (e^{2 x} + 1) + x

Add a constant to the solution

= - \frac{1}{2} e^{- 2 x} (e^{2 x} + 1) + x + C

y = 2^{(0.3 x - 7)} - 0.0625

y = x^{2} + 1

\frac{d}{d x} (2 1 + x)

f (x) = (x + 1)^{2}

y^{^{''}} + 324 y = sec (18 x)

What is the integral of (e^{2x}+1)/(e^{2x)} ?
The integral of (e^{2x}+1)/(e^{2x)} is -1/2 e^{-2x}(e^{2x}+1)+x+C