What is the integral of 1/(sqrt(2x+3)) ?

The integral of 1/(sqrt(2x+3)) is sqrt(2x+3)+C

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integral of 1/(sqrt(2x+3))

\int \frac{1}{2 x + 3} d x

2 x + 3 + C

Solution steps

\int \frac{1}{2 x + 3} d x

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 2 x + 3

= \frac{1}{2} \cdot 2 (2 x + 3)^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (2 x + 3)^{\frac{1}{2}} : 2 x + 3

= 2 x + 3

Add a constant to the solution

= 2 x + 3 + C

\frac{d}{d x} ((\frac{1}{2} x^{2} - 3)^{2})

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

y = x e^{- x}, y = 0, x = 4

x \to + 1 lim ((x^{2} - 9)^{\frac{1}{3}})

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

What is the integral of 1/(sqrt(2x+3)) ?
The integral of 1/(sqrt(2x+3)) is sqrt(2x+3)+C