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

The integral of xsin(1/3 x) is -3xcos(1/3 x)+9sin(1/3 x)+C

Popular >

integral of xsin(1/3 x)

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

- 3 x cos (\frac{1}{3} x) + 9 sin (\frac{1}{3} x) + C

Solution steps

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

Apply Integration By Parts

: - 3 x cos (\frac{1}{3} x) - \int - 3 cos (\frac{1}{3} x) d x

= - 3 x cos (\frac{1}{3} x) - \int - 3 cos (\frac{1}{3} x) d x

\int - 3 cos (\frac{1}{3} x) d x = - 9 sin (\frac{1}{3} x)

= - 3 x cos (\frac{1}{3} x) - (- 9 sin (\frac{1}{3} x))

Simplify

= - 3 x cos (\frac{1}{3} x) + 9 sin (\frac{1}{3} x)

Add a constant to the solution

= - 3 x cos (\frac{1}{3} x) + 9 sin (\frac{1}{3} x) + C

\frac{\partial}{\partial x} (z \cdot arctan (\frac{y}{x}))

y = x^{2}, (1, 1)

6 x - x^{2}

\frac{( 3 + 3 s )}{s ^{2} + 0.5}

\frac{( cos ( x ) )}{1 - sin ( x )}

What is the integral of xsin(1/3 x) ?
The integral of xsin(1/3 x) is -3xcos(1/3 x)+9sin(1/3 x)+C