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

The integral of x^{sqrt(2)}-3/(sqrt(x))+5/x is (sqrt(2)-1)x^{sqrt(2)+1}-6sqrt(x)+5ln|x|+C

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

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

(2 - 1) x^{2 + 1} - 6 x + 5 ln ∣ x ∣ + C

Solution steps

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

\int x^{2} d x = (2 - 1) x^{2 + 1}

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= (2 - 1) x^{2 + 1} - 6 x + 5 ln ∣ x ∣

Add a constant to the solution

= (2 - 1) x^{2 + 1} - 6 x + 5 ln ∣ x ∣ + C

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What is the integral of x^{sqrt(2)}-3/(sqrt(x))+5/x ?
The integral of x^{sqrt(2)}-3/(sqrt(x))+5/x is (sqrt(2)-1)x^{sqrt(2)+1}-6sqrt(x)+5ln|x|+C