What is the integral of sin(x)x ?

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

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integral of sin(x)x

\int sin (x) x d x

- x cos (x) + sin (x) + C

Solution steps

\int sin (x) x d x

Apply Integration By Parts

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

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

= - x cos (x) - (- sin (x))

Simplify

= - x cos (x) + sin (x)

Add a constant to the solution

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