What is the integral of 3/2 x^{1/2} ?

The integral of 3/2 x^{1/2} is x^{3/2}+C

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integral of 3/2 x^{1/2}

\int \frac{3}{2} x^{\frac{1}{2}} d x

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

Solution steps

\int \frac{3}{2} x^{\frac{1}{2}} d x

Take the constant out:

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

= \frac{3}{2} \cdot \int x^{\frac{1}{2}} d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{sin ( ln ( 4 x ^{2} ) )}{x} d x

x \to 1 lim (- 2 1 - x + 2)

\frac{d}{d x} (sin (x^{2} + 2 x))

x \to 0 lim (cos (x) ln (x))

f (x) = 4 sin (2 x)