What is the integral of sqrt(7x) ?

The integral of sqrt(7x) is sqrt(7) 2/3 x^{3/2}+C

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integral of sqrt(7x)

\int 7 x d x

7 \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

\int 7 x d x

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

= \int 7 x d x

Take the constant out:

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

= 7 \cdot \int x d x

Apply the Power Rule

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

= 7 \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 7 \frac{2}{3} x^{\frac{3}{2}} + C

y^{^{''}} - 2 y^{^{'}} + 1 = 0

\int 0. 4^{\frac{x}{2}} d x

\frac{d}{d x} (\frac{8 x}{( x ^{2} + 1 ) ^{2}})

x \to 1 lim (\frac{1}{( sec ( \frac{π x}{2} ) ( 1 - x ) )})

\frac{d y}{d x} = \frac{( e ^{x} - e ^{- x} )}{3 + 4 y}

What is the integral of sqrt(7x) ?
The integral of sqrt(7x) is sqrt(7) 2/3 x^{3/2}+C