What is the integral of xsin(1/6 x) ?

The integral of xsin(1/6 x) is -6xcos(1/6 x)+36sin(1/6 x)+C

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integral of xsin(1/6 x)

\int x sin (\frac{1}{6} x) d x

- 6 x cos (\frac{1}{6} x) + 36 sin (\frac{1}{6} x) + C

Solution steps

\int x sin (\frac{1}{6} x) d x

Apply Integration By Parts

: - 6 x cos (\frac{1}{6} x) - \int - 6 cos (\frac{1}{6} x) d x

= - 6 x cos (\frac{1}{6} x) - \int - 6 cos (\frac{1}{6} x) d x

\int - 6 cos (\frac{1}{6} x) d x = - 36 sin (\frac{1}{6} x)

= - 6 x cos (\frac{1}{6} x) - (- 36 sin (\frac{1}{6} x))

Simplify

= - 6 x cos (\frac{1}{6} x) + 36 sin (\frac{1}{6} x)

Add a constant to the solution

= - 6 x cos (\frac{1}{6} x) + 36 sin (\frac{1}{6} x) + C

\int \frac{4}{x - 4} d x

\frac{156}{x}, - 49 x + 189

\int \frac{( 4 + e ^{x} ) ^{2}}{e ^{x}} d x

y^{^{''}} + 4 y^{^{'}} + 7 y = 0, y (0) = - 2, y^{^{'}} (0) = 4

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

What is the integral of xsin(1/6 x) ?
The integral of xsin(1/6 x) is -6xcos(1/6 x)+36sin(1/6 x)+C