What is the integral of 3sqrt(x^2) ?

The integral of 3sqrt(x^2) is (3x^2)/2+C

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integral of 3sqrt(x^2)

\int 3 x^{2} d x

\frac{3 x ^{2}}{2} + C

Solution steps

\int 3 x^{2} d x

Take the constant out:

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

= 3 \cdot \int x^{2} d x

x^{2} = (x),

assuming

x \geq 0

= 3 \cdot \int x d x

Apply the Power Rule

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

= 3 \cdot \frac{x ^{2}}{2}

Multiply fractions:

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

= \frac{3 x ^{2}}{2}

Add a constant to the solution

= \frac{3 x ^{2}}{2} + C

\frac{\partial}{\partial y} (ln (1 + x y))

\int \frac{1}{x ^{2} + 4 x + 1} d x

\frac{\partial}{\partial x} (5 x y (9 - x - y))

e^{x} - 3 x

\frac{\partial}{\partial x} (8)