What is the integral of-15x^{2/3} ?

The integral of-15x^{2/3} is -9x^{5/3}+C

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integral of-15x^{2/3}

\int - 15 x^{\frac{2}{3}} d x

- 9 x^{\frac{5}{3}} + C

Solution steps

\int - 15 x^{\frac{2}{3}} d x

Take the constant out:

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

= - 15 \cdot \int x^{\frac{2}{3}} d x

Apply the Power Rule

: \frac{3}{5} x^{\frac{5}{3}}

= - 15 \cdot \frac{3}{5} x^{\frac{5}{3}}

Simplify

- 15 \cdot \frac{3}{5} x^{\frac{5}{3}} : - 9 x^{\frac{5}{3}}

= - 9 x^{\frac{5}{3}}

Add a constant to the solution

= - 9 x^{\frac{5}{3}} + C

\frac{d y}{d x} - y x = 0

x \to \infty lim (8 x^{3})

2 y^{^{''}} - 3 y^{^{'}} + y = e^{2 x} + sin (x)

f (x) = sin (x^{2})

f (x) = x^{\frac{7}{2}} (3 - 4 x^{3})