What is the integral of 9xsqrt(y) ?

The integral of 9xsqrt(y) is 6xy^{3/2}+C

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integral of 9xsqrt(y)

\int 9 x y d y

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

Solution steps

\int 9 x y d y

Take the constant out:

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

= 9 x \cdot \int y d y

Apply the Power Rule

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

= 9 x \frac{2}{3} y^{\frac{3}{2}}

Simplify

9 x \frac{2}{3} y^{\frac{3}{2}} : 6 x y^{\frac{3}{2}}

= 6 x y^{\frac{3}{2}}

Add a constant to the solution

= 6 x y^{\frac{3}{2}} + C

x \to \infty lim (x - 4)

\frac{d}{d x} (- e^{c o s (x)} sin (x))

y = 3^{1 - x}