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

The integral of (cos(x)+1/(sqrt(x))-1) is sin(x)+2sqrt(x)-x+C

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

\int (cos (x) + \frac{1}{x} - 1) d x

sin (x) + 2 x - x + C

Solution steps

\int cos (x) + \frac{1}{x} - 1 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 cos (x) d x + \int \frac{1}{x} d x - \int 1 d x

\int cos (x) d x = sin (x)

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

\int 1 d x = x

= sin (x) + 2 x - x

Add a constant to the solution

= sin (x) + 2 x - x + C

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