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

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

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

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

Si (x) - x + C

Solution steps

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

Expand

\frac{sin ( x ) - x}{x} : \frac{sin ( x )}{x} - 1

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

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

\int 1 d x = x

= Si (x) - x

Add a constant to the solution

= Si (x) - x + C

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