What is the integral of 21sqrt(y) ?

The integral of 21sqrt(y) is 14y^{3/2}+C

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integral of 21sqrt(y)

\int 21 y d y

14 y^{\frac{3}{2}} + C

Solution steps

\int 21 y d y

Take the constant out:

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

= 21 \cdot \int y d y

Apply the Power Rule

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

= 21 \cdot \frac{2}{3} y^{\frac{3}{2}}

Simplify

21 \cdot \frac{2}{3} y^{\frac{3}{2}} : 14 y^{\frac{3}{2}}

= 14 y^{\frac{3}{2}}

Add a constant to the solution

= 14 y^{\frac{3}{2}} + C

y^{^{''}} - \frac{2}{r} y^{^{'}} + \frac{2}{r ^{2}} y = 0, y (1) = 1, y (2) = 0

\int 12 x^{2} - 48 x + 36 d x

x \to 3 lim (\frac{3 x ^{2} - 4 x - 15}{x ^{2} - 5 x + 6})

x^{2} + 2 x + 1, 3 x + 3

\frac{d}{d x} (\frac{c}{x ^{2}})