What is the integral of (sqrt(2x))/x+3/(x^5) ?

The integral of (sqrt(2x))/x+3/(x^5) is sqrt(2/x)x+sqrt(2)sqrt(x)-3/(4x^4)+C

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integral of (sqrt(2x))/x+3/(x^5)

\int \frac{2 x}{x} + \frac{3}{x ^{5}} d x

\frac{2}{x} x + 2 x - \frac{3}{4 x ^{4}} + C

Solution steps

\int \frac{2 x}{x} + \frac{3}{x ^{5}} 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{2 x}{x} d x + \int \frac{3}{x ^{5}} d x

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

\int \frac{3}{x ^{5}} d x = - \frac{3}{4 x ^{4}}

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

Add a constant to the solution

= \frac{2}{x} x + 2 x - \frac{3}{4 x ^{4}} + C

What is the integral of (sqrt(2x))/x+3/(x^5) ?
The integral of (sqrt(2x))/x+3/(x^5) is sqrt(2/x)x+sqrt(2)sqrt(x)-3/(4x^4)+C