What is the integral of 12sqrt(x) ?

The integral of 12sqrt(x) is 8x^{3/2}+C

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integral of 12sqrt(x)

\int 12 x d x

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

Solution steps

\int 12 x d x

Take the constant out:

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

= 12 \cdot \int x d x

Apply the Power Rule

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

= 12 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

12 \cdot \frac{2}{3} x^{\frac{3}{2}} : 8 x^{\frac{3}{2}}

= 8 x^{\frac{3}{2}}

Add a constant to the solution

= 8 x^{\frac{3}{2}} + C

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

x \to π lim (tan (\frac{2}{3} x))

f (x) = \frac{x ^{2}}{2 + x}

n \to \infty lim (\frac{n}{1})

\int e^{3 x} cos (4 x) d x