What is the integral of (sqrt(x)-xcos(a))/x ?

The integral of (sqrt(x)-xcos(a))/x is 2sqrt(x)-cos(a)x+C

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integral of (sqrt(x)-xcos(a))/x

\int \frac{x - x cos ( a )}{x} d x

2 x - cos (a) x + C

Solution steps

\int \frac{x - x cos ( a )}{x} d x

Expand

\frac{x - x cos ( a )}{x} : \frac{1}{x} - cos (a)

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

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

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

= 2 x - cos (a) x

Add a constant to the solution

= 2 x - cos (a) x + C

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