What is the integral of xsin(x)) ?

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

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integral of xsin(x))

\int x d (sin (x)) d x

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

Solution steps

\int x d 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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\int cos (2 t + 1) d t

\int (2 x^{2} + 3) arctan (x) d x

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