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

The integral of (xcos(x)-sin(x))/x is sin(x)-\Si(x)+C

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integral of (xcos(x)-sin(x))/x

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

sin (x) - Si (x) + C

Solution steps

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

Expand

\frac{x cos ( x ) - sin ( x )}{x} : cos (x) - \frac{sin ( x )}{x}

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

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

\int \frac{sin ( x )}{x} d x = Si (x)

= sin (x) - Si (x)

Add a constant to the solution

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

What is the integral of (xcos(x)-sin(x))/x ?
The integral of (xcos(x)-sin(x))/x is sin(x)-\Si(x)+C