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Popular >

integral of 1-ye^{-x}

Solution

\int 1 - y e^{- x} d x

Solution

x + y e^{- x} + C

Solution steps

\int 1 - y 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 1 d x - \int y e^{- x} d x

\int 1 d x = x

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

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

Simplify

= x + y e^{- x}

Add a constant to the solution

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

Graph

Popular Examples

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

\int \frac{e ^{3 x}}{2 + e ^{3 x}} d x

integral of (2x-1)^8

\int (2 x - 1)^{8} d x

integral of \sqrt[3]{1-4y}

\int 3 1 - 4 y d y

integral of 1/(\sqrt[3]{(4-x)^2)}

\int \frac{1}{3 ( 4 - x ) ^{2}} d x

integral of e^x(1+4e^x)^5

\int e^{x} (1 + 4 e^{x})^{5} d x

Frequently Asked Questions (FAQ)

What is the integral of 1-ye^{-x} ?
The integral of 1-ye^{-x} is x+ye^{-x}+C