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

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

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integral of sqrt(2x^2)

\int 2 x^{2} d x

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

Solution steps

\int 2 x^{2} d x

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

= \int 2 x^{2} d x

Take the constant out:

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

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

x^{2} = (x),

assuming

x \geq 0

= 2 \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

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f (x) = arcsin (\frac{x}{2})

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