What is the integral of (3-2/(x^3)+1/(sqrt(x))) ?

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

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integral of (3-2/(x^3)+1/(sqrt(x)))

\int (3 - \frac{2}{x ^{3}} + \frac{1}{x}) d x

3 x + \frac{1}{x ^{2}} + 2 x + C

Solution steps

\int 3 - \frac{2}{x ^{3}} + \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 d x - \int \frac{2}{x ^{3}} d x + \int \frac{1}{x} d x

\int 3 d x = 3 x

\int \frac{2}{x ^{3}} d x = - \frac{1}{x ^{2}}

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

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

Simplify

= 3 x + \frac{1}{x ^{2}} + 2 x

Add a constant to the solution

= 3 x + \frac{1}{x ^{2}} + 2 x + C

\int_{0}^{1} 2 x 1 + 4 x^{2} d x

\frac{d}{d t} (- cos (t))

\int_{- 2}^{3} (x^{3} - 4 x) d x

x + 2, x^{2}, 0

9 x

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