What is the integral of ((e^{3x}+1))/((e^x+1)) ?

The integral of ((e^{3x}+1))/((e^x+1)) is 1/2 e^{2x}-e^x+x+C

Popular >

integral of ((e^{3x}+1))/((e^x+1))

\int \frac{( e ^{3 x} + 1 )}{( e ^{x} + 1 )} d x

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

Solution steps

\int \frac{e ^{3 x} + 1}{e ^{x} + 1} d x

Simplify

\frac{e ^{3 x} + 1}{e ^{x} + 1} : e^{2 x} - e^{x} + 1

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int e^{x} d x = e^{x}

\int 1 d x = x

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

Add a constant to the solution

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

\int \frac{2}{e ^{- t}} d t

\int \frac{ln ( 1 + x ) - ln ( x )}{x ( x + 1 )} d x

\int \frac{1}{6 x - 5} d x

\int \frac{2}{2 x ^{2}} d x

\int sec^{5} (7 x) tan (7 x) d x

What is the integral of ((e^{3x}+1))/((e^x+1)) ?
The integral of ((e^{3x}+1))/((e^x+1)) is 1/2 e^{2x}-e^x+x+C