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Popular >

integral of e^x-xe^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} d x - \int x e^{x} d x

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

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

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

derivative of f(x)=-(42)/((x+4)^4)derivative of

f (x) = - \frac{42}{( x + 4 ) ^{4}}

integral from 0 to 5 of 1/(x^{20/19)}

\int_{0}^{5} \frac{1}{x ^{\frac{20}{19}}} d x

derivative of (x^2/(x^3+4))

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

(\partial)/(\partial x)(5y-x+y^2sin(y))

\frac{\partial}{\partial x} (5 y - x + y^{2} sin (y))

(dy)/(dx)=y^3xe^{x^2}

\frac{d y}{d x} = y^{3} x e^{x^{2}}

Frequently Asked Questions (FAQ)

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