What is the integral of xsin(1/9 x) ?

The integral of xsin(1/9 x) is -9xcos(1/9 x)+81sin(1/9 x)+C

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integral of xsin(1/9 x)

\int x sin (\frac{1}{9} x) d x

- 9 x cos (\frac{1}{9} x) + 81 sin (\frac{1}{9} x) + C

Solution steps

\int x sin (\frac{1}{9} x) d x

Apply Integration By Parts

: - 9 x cos (\frac{1}{9} x) - \int - 9 cos (\frac{1}{9} x) d x

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

\int - 9 cos (\frac{1}{9} x) d x = - 81 sin (\frac{1}{9} x)

= - 9 x cos (\frac{1}{9} x) - (- 81 sin (\frac{1}{9} x))

Simplify

= - 9 x cos (\frac{1}{9} x) + 81 sin (\frac{1}{9} x)

Add a constant to the solution

= - 9 x cos (\frac{1}{9} x) + 81 sin (\frac{1}{9} x) + C

\int_{- 4}^{4} x (16 - x^{2}) d x

x \to 6 lim (5 x + 6)

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

\int_{1}^{2} 5 4 x^{2} - 3 d x

(\frac{1}{t - 1})^{^{'}}

What is the integral of xsin(1/9 x) ?
The integral of xsin(1/9 x) is -9xcos(1/9 x)+81sin(1/9 x)+C