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

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

Popular >

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

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

x (x + 2) + C

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

: 2 x (3 x + 2) - \int 6 x d x

= \frac{1}{2} (2 x (3 x + 2) - \int 6 x d x)

\int 6 x d x = 4 x^{\frac{3}{2}}

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

Simplify

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

= x (x + 2)

Add a constant to the solution

= x (x + 2) + C

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

\int \frac{t ^{2}}{t ^{2} + 2} d t

\int \frac{- 4 x - 1}{7 ( x ^{2} - x + 1 )} d x

\int \frac{1}{sin ( \frac{1}{2} ) x cot ( \frac{1}{2} ) x} d x

\int \frac{1}{( 3 x + 4 )} d x

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