What is the integral of x/(sqrt(2)) ?

The integral of x/(sqrt(2)) is (x^2)/(2sqrt(2))+C

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integral of x/(sqrt(2))

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{x ^{2}}{2}

Simplify

\frac{1}{2} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{2 2}

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

Add a constant to the solution

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

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