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Popular >

integral of xe^x+e^x

Solution

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

Solution

e^{x} 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

Add a constant to the solution

= e^{x} x + C

Popular Examples

integral of 2sin^2(y)

\int 2 sin^{2} (y) d y

(dy)/(dx)=(y^2-1)/(x^2-1),y(2)=-1

\frac{d y}{d x} = \frac{y ^{2} - 1}{x ^{2} - 1}, y (2) = - 1

derivative of ln^4(x^3+2x-e^{-3x})

\frac{d}{d x} (ln^{4} (x^{3} + 2 x - e^{- 3 x}))

(\partial)/(\partial y)(1+ln(xy))

\frac{\partial}{\partial y} (1 + ln (x y))

integral from-1 to 1 of 3/(x^2)

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