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[tex] \int x sin (2x) dx =?[/tex]

[tex]u=2x[/tex]

[tex]du=2dx[/tex]

[tex]\int \frac{u}{2} sin(u) \frac{du}{2}[/tex]

[tex]\frac{1}{4} \int usin(u)du[/tex]

[tex]\frac{1}{4} (\frac{u^2}{2}sin(u)+u(-cos(u)))[/tex]

[tex]\frac{2x^2}{4} sin(2x)-\frac{1}{2} cos(2x)+C[/tex]

is this correct?

[tex]u=2x[/tex]

[tex]du=2dx[/tex]

[tex]\int \frac{u}{2} sin(u) \frac{du}{2}[/tex]

[tex]\frac{1}{4} \int usin(u)du[/tex]

[tex]\frac{1}{4} (\frac{u^2}{2}sin(u)+u(-cos(u)))[/tex]

[tex]\frac{2x^2}{4} sin(2x)-\frac{1}{2} cos(2x)+C[/tex]

is this correct?

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