What is the integral of xsin(10x) ?

The integral of xsin(10x) is -1/10 xcos(10x)+1/100 sin(10x)+C

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integral of xsin(10x)

\int x sin (10 x) d x

- \frac{1}{10} x cos (10 x) + \frac{1}{100} sin (10 x) + C

Solution steps

\int x sin (10 x) d x

Apply Integration By Parts

: - \frac{1}{10} x cos (10 x) - \int - \frac{1}{10} cos (10 x) d x

= - \frac{1}{10} x cos (10 x) - \int - \frac{1}{10} cos (10 x) d x

\int - \frac{1}{10} cos (10 x) d x = - \frac{1}{100} sin (10 x)

= - \frac{1}{10} x cos (10 x) - (- \frac{1}{100} sin (10 x))

Simplify

= - \frac{1}{10} x cos (10 x) + \frac{1}{100} sin (10 x)

Add a constant to the solution

= - \frac{1}{10} x cos (10 x) + \frac{1}{100} sin (10 x) + C

\int 0.4 t d t

x \to 0 lim (x^{2} - 4 x + 2)

\int 4 e^{2 x} + 3 d x

\frac{\partial}{\partial x} (\frac{( x y )}{( x - y )})

x \to 0 lim (x + ln (x))

What is the integral of xsin(10x) ?
The integral of xsin(10x) is -1/10 xcos(10x)+1/100 sin(10x)+C