What is the integral of 6x^{3/2} ?

The integral of 6x^{3/2} is 12/5 x^{5/2}+C

Popular >

integral of 6x^{3/2}

\int 6 x^{\frac{3}{2}} d x

\frac{12}{5} x^{\frac{5}{2}} + C

Solution steps

\int 6 x^{\frac{3}{2}} d x

Take the constant out:

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

= 6 \cdot \int x^{\frac{3}{2}} d x

Apply the Power Rule

: \frac{2}{5} x^{\frac{5}{2}}

= 6 \cdot \frac{2}{5} x^{\frac{5}{2}}

Simplify

6 \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{12}{5} x^{\frac{5}{2}}

= \frac{12}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{12}{5} x^{\frac{5}{2}} + C

x \to \infty lim (4^{x} + 5)

\frac{d}{d x} (\frac{3}{x ^{2}} + \frac{1}{x})

\int \frac{1}{x ^{2} - 2 x + 10} d x

49 y^{^{''}} + 28 y^{^{'}} + 4 y = 0

16 y^{^{''}} - 40 y^{^{'}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = - 94