What is the integral of (1 [xsin(x)]) ?

The integral of (1 [xsin(x)]) is d(-xcos(x)+sin(x))+C

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integral of (1 [xsin(x)])

\int (\frac{d}{1} [x sin (x)]) d x

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

Solution steps

\int \frac{d}{1} [x sin (x)] d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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What is the integral of (1 [xsin(x)]) ?
The integral of (1 [xsin(x)]) is d(-xcos(x)+sin(x))+C