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Popular >

integral of x*e^2

Solution

\int x \cdot e^{2} d x

Solution

\frac{e ^{2} x ^{2}}{2} + C

Solution steps

\int x e^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{2} \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= e^{2} \frac{x ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{2} x ^{2}}{2}

Add a constant to the solution

= \frac{e ^{2} x ^{2}}{2} + C

Popular Examples

derivative of (x-4/(x^2+1))

\frac{d}{d x} (\frac{x - 4}{x ^{2} + 1})

sum from n=0 to infinity of (-1/2)^{n+1}

n = 0 \sum \infty (- \frac{1}{2})^{n + 1}

derivative of In(3x)

\frac{d}{d x} (I n (3 x))

integral of x^{-1/2}e^{-x}

\int x^{- \frac{1}{2}} e^{- x} d x

(\partial)/(\partial y)(x^{0.5}y^{0.5})

\frac{\partial}{\partial y} (x^{0.5} y^{0.5})

Frequently Asked Questions (FAQ)

What is the integral of x*e^2 ?
The integral of x*e^2 is (e^2x^2)/2+C