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Popular >

integral of (x*e^x)

Solution

\int (x \cdot e^{x}) d x

Solution

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

Solution steps

\int x e^{x} d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

Popular Examples

d/(d{x)}({y}{z}e^{{x}{z}})

\frac{d}{d x} (y z e^{x z})

derivative of arcsin(4x^5)

\frac{d}{d x} (arcsin (4 x^{5}))

implicit (dy)/(dx),9sin(x)+cos(y)=sin(x)cos(y)implicit derivative

\frac{d y}{d x}, 9 sin (x) + cos (y) = sin (x) cos (y)

integral from 0 to 1 of xe^{10x}

\int_{0}^{1} x e^{10 x} d x

y^{''}-4y^'+2y=e^{-t},y(0)=0,y^'(0)=1

y^{^{''}} - 4 y^{^{'}} + 2 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1

Frequently Asked Questions (FAQ)

What is the integral of (x*e^x) ?
The integral of (x*e^x) is e^xx-e^x+C