How do you find $\int x sin (6 x)$ $int xsin(6x)$ ?

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Answer 1 · 2015-11-21T12:16:02

$\frac{1}{36} sin 6 x - \frac{1}{6} x cos 6 x$ $1 / 36 sin 6x-1/6 x cos 6x$

we want to disappear with "x" factor.

$u = x, d u = d x$ $u = x, du = dx$

$d v = sin 6 x \Rightarrow v = \int sin 6 x d x$ $dv = sin 6x Rightarrow v = int sin 6x text{ d}x$

$A = \int u d v = x v - \int v d x$ $A = int u text{ d}v = xv - int v text{ d} x$

$w = 6 x \Rightarrow \frac{d w}{6} = d x$ $w = 6x Rightarrow frac{dw}{6} = dx$

$v = \int sin w \frac{d w}{6} = - \frac{1}{6} cos w$ $v = int sin w (dw)/6 = - 1/6 cos w$

$A = - \frac{x}{6} cos 6 x + \int \frac{1}{6} (cos w) \frac{d w}{6}$ $A = -x/6 cos 6x + int 1/6 (cos w) (dw)/6$

$A = - \frac{x}{6} cos 6 x + \frac{1}{36} sin w$ $A = -x/6 cos 6x + 1 / 36 sin w$

How do you find ∫xsin(6x)int xsin(6x) ?