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Popular >

integral of e^xx-e^x

Solution

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

Solution

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

Solution steps

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

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

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

= e^{x} x - e^{x} - e^{x}

Simplify

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

Add a constant to the solution

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

Popular Examples

limit as x approaches 5 of x^3

x \to 5 lim (x^{3})

integral of 1/(x^2-2x+5)

\int \frac{1}{x ^{2} - 2 x + 5} d x

y^{''}-y^'-2y=7e^{-t}

y^{^{''}} - y^{^{'}} - 2 y = 7 e^{- t}

y^{''}+16y=2csc^2(4t)

y^{^{''}} + 16 y = 2 csc^{2} (4 t)

(\partial)/(\partial x)(7xy^6)

\frac{\partial}{\partial x} (7 x y^{6})

Frequently Asked Questions (FAQ)

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