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Popular Calculus >

integral of xe^x-e^x

Solution

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

Solution

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

Solution steps

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

\int x e^{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

Graph

Popular Examples

(dy)/(dx)=2xy+6/(sqrt(pi))

\frac{d y}{d x} = 2 x y + \frac{6}{π}

integral of 1/(x^4sqrt(9-x^2))

\int \frac{1}{x ^{4} 9 - x ^{2}} d x

(dy)/(dt)= 1/2 t

\frac{d y}{d t} = \frac{1}{2} t

y^{''}+6y^'+9y=12e^{-3x}

y^{^{''}} + 6 y^{^{'}} + 9 y = 12 e^{- 3 x}

integral of 50sin(120pi)x

\int 50 sin (120 π) x d x

Frequently Asked Questions (FAQ)

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