What is the integral of 3xsin(1/6 x) ?

The integral of 3xsin(1/6 x) is 3(-6xcos(1/6 x)+36sin(1/6 x))+C

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integral of 3xsin(1/6 x)

\int 3 x sin (\frac{1}{6} x) d x

3 (- 6 x cos (\frac{1}{6} x) + 36 sin (\frac{1}{6} x)) + C

Solution steps

\int 3 x sin (\frac{1}{6} x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \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

= 3 (- 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)

= 3 (- 6 x cos (\frac{1}{6} x) - (- 36 sin (\frac{1}{6} x)))

Simplify

= 3 (- 6 x cos (\frac{1}{6} x) + 36 sin (\frac{1}{6} x))

Add a constant to the solution

= 3 (- 6 x cos (\frac{1}{6} x) + 36 sin (\frac{1}{6} x)) + C

f (x) = - \frac{1}{x}

n = 1 \sum \infty 6 sin (\frac{1}{n})

\frac{12 ( s + 1 )}{s ( s ^{2} + 9 )}

\frac{\partial}{\partial x} (cos (3 y))

\frac{d}{d x} (\frac{x}{x - 6})

What is the integral of 3xsin(1/6 x) ?
The integral of 3xsin(1/6 x) is 3(-6xcos(1/6 x)+36sin(1/6 x))+C