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

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

Popular >

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

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

x (x + 4) + C

Solution steps

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

Apply Integration By Parts

: 2 x (3 x + 4) - \int 6 x d x

= \frac{1}{2} (2 x (3 x + 4) - \int 6 x d x)

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

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

Simplify

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

= x (x + 4)

Add a constant to the solution

= x (x + 4) + C

\int \frac{e ^{2 x}}{2 x} d x

\int \frac{x - 3}{3 - 2 x - x ^{2}} d x

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

\int e^{- 2 \cdot x} d x

\int \frac{x}{x ^{2} + 2500} d x

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