What is the integral of (xsin(x)) ?

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

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integral of (xsin(x))

\int (x sin (x)) d x

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

Solution steps

\int x sin (x) d x

Apply Integration By Parts

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

= - 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

y = \frac{2 x}{4 + x ^{2}}

\frac{d x}{d t} = \frac{2}{x}

x \to 6 lim ((x + 1)^{2})

\int \frac{1}{( 3 x + 5 ) ^{4}} d x

\frac{\partial}{\partial x} ((x + 2)^{2})

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