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

\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

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