∫ xsin3x dx=x( cos3x)1/3 ∫1×( cos3x)1/3dx #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; = xcos3x3 ...

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Integration by Parts

∫xsin 3xdx

Question

$\int x sin 3 x d x$

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Solution

$\int x s i n 3 x d x = x (- c o s 3 x) \frac{1}{3} - \int 1 \times (- c o s 3 x) \frac{1}{3} d x$

$= \frac{- x c o s 3 x}{3} + \frac{s i n 3 x}{9} + c$

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