What is the integral of 2/(sqrt(4+3x)) ?

The integral of 2/(sqrt(4+3x)) is 4/3 sqrt(4+3x)+C

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integral of 2/(sqrt(4+3x))

\int \frac{2}{4 + 3 x} d x

\frac{4}{3} 4 + 3 x + C

Solution steps

\int \frac{2}{4 + 3 x} d x

Take the constant out:

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

= 2 \cdot \int \frac{1}{4 + 3 x} d x

Apply u-substitution

: \int \frac{1}{3 u} d u

= 2 \cdot \int \frac{1}{3 u} d u

Take the constant out:

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

= 2 \cdot \frac{1}{3} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= 2 \cdot \frac{1}{3} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 4 + 3 x

= 2 \cdot \frac{1}{3} \cdot 2 (4 + 3 x)^{\frac{1}{2}}

Simplify

2 \cdot \frac{1}{3} \cdot 2 (4 + 3 x)^{\frac{1}{2}} : \frac{4}{3} 4 + 3 x

= \frac{4}{3} 4 + 3 x

Add a constant to the solution

= \frac{4}{3} 4 + 3 x + C

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What is the integral of 2/(sqrt(4+3x)) ?
The integral of 2/(sqrt(4+3x)) is 4/3 sqrt(4+3x)+C