What is the integral of 3sqrt(x)+1/(sqrt(x))-1/x ?

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

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integral of 3sqrt(x)+1/(sqrt(x))-1/x

\int 3 x + \frac{1}{x} - \frac{1}{x} d x

2 x^{\frac{3}{2}} + 2 x - ln ∣ x ∣ + C

Solution steps

\int 3 x + \frac{1}{x} - \frac{1}{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 3 x d x + \int \frac{1}{x} d x - \int \frac{1}{x} d x

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

\int \frac{1}{x} d x = 2 x

\int \frac{1}{x} d x = ln ∣ x ∣

= 2 x^{\frac{3}{2}} + 2 x - ln ∣ x ∣

Add a constant to the solution

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

\int \frac{1}{x x ^{2} - 25} d x

h \to 0 lim (\frac{3 ^{h} - 1}{h})

f (x) = \frac{1}{x}, at x = 25

f (x) = (4 x - 3)^{\frac{1}{2}}

y^{^{''}} + y = - sin (2 x), y (0) = 0

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