What is $int xsinx$ ?

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Answer 1 · 2015-11-08T18:17:24

$int x sin x dx = sin(x) - x cos(x) + C$

Use the following:

$d/dx x = 1$

$d/dx sin(x) = cos(x)$

$d/dx cos(x) = -sin(x)$

$d/dx (f(x)g(x)) = f'(x)g(x) + f(x)g'(x)$

To find:

$d/dx (sin(x) - x cos(x) + C) = color(red)(cancel(color(black)(cos(x)))) - color(red)(cancel(color(black)(cos(x)))) + x sin(x) = x sin(x)$

Hence:

$int x sin x dx = sin(x) - x cos(x) + C$

What is int xsinxint xsinx?