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Popular >

integral of e x/2

Solution

\int e \frac{x}{2} d x

Solution

\frac{e x ^{2}}{4} + C

Solution steps

\int e \frac{x}{2} d x

Take the constant out:

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

= e \frac{1}{2} \cdot \int x d x

e \frac{1}{2} = \frac{e}{2}

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

Apply the Power Rule

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

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

Simplify

\frac{e}{2} \cdot \frac{x ^{2}}{2} : \frac{e x ^{2}}{4}

= \frac{e x ^{2}}{4}

Add a constant to the solution

= \frac{e x ^{2}}{4} + C

Popular Examples

limit as x approaches 3+of (3-x)/(|x-3|)

x \to 3 + lim (\frac{3 - x}{∣ x - 3 ∣})

y^{^{'}} = ln (x)

laplacetransform f(t)=(1+e^{4t})^2 laplace transform

f (t) = (1 + e^{4 t})^{2}

integral of (3x+1)/(x(x+1)^2)

\int \frac{3 x + 1}{x ( x + 1 ) ^{2}} d x

laplacetransform e^{-2t-5}laplace transform

e^{- 2 t - 5}

Frequently Asked Questions (FAQ)

What is the integral of e x/2 ?
The integral of e x/2 is (ex^2)/4+C