What is the integral of (e^x+2e^{-3x}-e^{5x}) ?

The integral of (e^x+2e^{-3x}-e^{5x}) is e^x-2/3 e^{-3x}-1/5 e^{5x}+C

Popular >

integral of (e^x+2e^{-3x}-e^{5x})

\int (e^{x} + 2 e^{- 3 x} - e^{5 x}) d x

e^{x} - \frac{2}{3} e^{- 3 x} - \frac{1}{5} e^{5 x} + C

Solution steps

\int e^{x} + 2 e^{- 3 x} - e^{5 x} 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^{x} d x + \int 2 e^{- 3 x} d x - \int e^{5 x} d x

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

\int 2 e^{- 3 x} d x = - \frac{2}{3} e^{- 3 x}

\int e^{5 x} d x = \frac{1}{5} e^{5 x}

= e^{x} - \frac{2}{3} e^{- 3 x} - \frac{1}{5} e^{5 x}

Add a constant to the solution

= e^{x} - \frac{2}{3} e^{- 3 x} - \frac{1}{5} e^{5 x} + C

\int sec (t) (2 sec (t) + 9 tan (t)) d t

\int 7 x^{2} ln (4 x) d x

\int (3 x + 4)^{10} d x

\int arctan (x - 1) d x

\int \frac{2 + 8 x}{1 + x ^{2}} d x

What is the integral of (e^x+2e^{-3x}-e^{5x}) ?
The integral of (e^x+2e^{-3x}-e^{5x}) is e^x-2/3 e^{-3x}-1/5 e^{5x}+C