Question

$\int x*sin3x\, dx$

Answer 1

∫ $x*sin3x d x$

$x*(- \frac{cos(3x)}{3} )- \int\limits - \frac{cos (3x)}{3} dx$

$x*(- \frac{cos (3x)}{3})-1 (- \frac{1}{3} ) * \int\limits cos(3x) dx$


$x*(- \frac{cos(3x)}{3} + \frac{1}{3} * \int\limits \frac{cos(t)}{3} dt$

$x*(- \frac{cos(3x)}{3} + \frac{1}{3} * \frac{1}{3} * \int\limits cos (t) dt$


[tex]x*(- \frac{cos(3x)}{3} ) + \frac{1}{9} * sin(t) [/tex]

$x*(- \frac{cos(3x)}{3} + \frac{1}{9} *sin(3x)$

$- \frac{x*cos(3x)}{3} + \frac{sin (3x)}{9}$

[tex]- \frac{x*cos(3x)}{3} + \frac{sin(3x)}{9} +C [/tex]


unde C ∈ R