What is the integral of ((7x+3)/(sqrt(x))) ?

The integral of ((7x+3)/(sqrt(x))) is 2sqrt(x)(7x+3)-28/3 x^{3/2}+C

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integral of ((7x+3)/(sqrt(x)))

\int (\frac{7 x + 3}{x}) d x

2 x (7 x + 3) - \frac{28}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{7 x + 3}{x} d x

Apply Integration By Parts

: 2 x (7 x + 3) - \int 14 x d x

= 2 x (7 x + 3) - \int 14 x d x

\int 14 x d x = \frac{28}{3} x^{\frac{3}{2}}

= 2 x (7 x + 3) - \frac{28}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 2 x (7 x + 3) - \frac{28}{3} x^{\frac{3}{2}} + C

\frac{\partial}{\partial x} (ln (x) - 1)

\int sec (x) - cos (x) d x

(4, - 7), (8, - 7)

f (x) = x ln (x) - x

\frac{1}{2} ln (x)

What is the integral of ((7x+3)/(sqrt(x))) ?
The integral of ((7x+3)/(sqrt(x))) is 2sqrt(x)(7x+3)-28/3 x^{3/2}+C