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Popular >

integral of 2-e^{-x}

Solution

\int 2 - e^{- x} d x

Solution

2 x + e^{- x} + C

Solution steps

\int 2 - e^{- 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 2 d x - \int e^{- x} d x

\int 2 d x = 2 x

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

= 2 x - (- e^{- x})

Simplify

= 2 x + e^{- x}

Add a constant to the solution

= 2 x + e^{- x} + C

Popular Examples

integral of 16tan^2(x)sec(x)

\int 16 tan^{2} (x) sec (x) d x

integral of (7t^2)/2

\int \frac{7 t ^{2}}{2} d t

integral of 1/(t^{7/4)}

\int \frac{1}{t ^{\frac{7}{4}}} d t

integral of (2sec^2(x)-8sec^2(5x))

\int (2 sec^{2} (x) - 8 sec^{2} (5 x)) d x

integral of 1/(sqrt(9-x^2-8x))

\int \frac{1}{9 - x ^{2} - 8 x} d x

Frequently Asked Questions (FAQ)

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