What is the integral of xsin(1/10 x) ?

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

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integral of xsin(1/10 x)

\int x sin (\frac{1}{10} x) d x

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

Solution steps

\int x sin (\frac{1}{10} x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int x + 1 ln (x + 1) d x

\int 5 x (2 + 3 x^{2})^{8} d x

\frac{10}{s ^{3} + s ^{2} + 10 s}

\frac{d}{d x} ((x^{2} + 1)^{2 x - x^{2}})

\frac{d}{d y} (- arctan (\frac{x}{y}))

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