What is the integral of (2^3)/(2*y^{1/2)} ?

The integral of (2^3)/(2*y^{1/2)} is 8y^{1/2}+C

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integral of (2^3)/(2*y^{1/2)}

integral

\frac{2 ^{3}}{2 \cdot y ^{\frac{1}{2}}}

8 y^{\frac{1}{2}} + C

Solution steps

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

Take the constant out:

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

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

\frac{2 ^{3}}{2} = 4

= 4 \cdot \int \frac{1}{y ^{\frac{1}{2}}} d y

Apply the Power Rule

: 2 y^{\frac{1}{2}}

= 4 \cdot 2 y^{\frac{1}{2}}

Simplify

= 8 y^{\frac{1}{2}}

Add a constant to the solution

= 8 y^{\frac{1}{2}} + C

e^{x} - 1

(x + 1) e^{x}

sin (2 x - 1)

1 + cos (x)

\frac{( 2 x + 3 )}{( 3 x + 4 )}

What is the integral of (2^3)/(2*y^{1/2)} ?
The integral of (2^3)/(2*y^{1/2)} is 8y^{1/2}+C