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

The integral of 3/(sqrt(x))+(xsqrt(x))/4+C is 6sqrt(x)+1/10 x^{5/2}+Cx+C

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integral of 3/(sqrt(x))+(xsqrt(x))/4+C

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

6 x + \frac{1}{10} x^{\frac{5}{2}} + C x + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{3}{x} d x = 6 x

\int \frac{x x}{4} d x = \frac{1}{10} x^{\frac{5}{2}}

\int C d x = C x

= 6 x + \frac{1}{10} x^{\frac{5}{2}} + C x

Add a constant to the solution

= 6 x + \frac{1}{10} x^{\frac{5}{2}} + C x + C

What is the integral of 3/(sqrt(x))+(xsqrt(x))/4+C ?
The integral of 3/(sqrt(x))+(xsqrt(x))/4+C is 6sqrt(x)+1/10 x^{5/2}+Cx+C