What is the integral of xsin(1/8 x) ?

The integral of xsin(1/8 x) is -8xcos(1/8 x)+64sin(1/8 x)+C

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integral of xsin(1/8 x)

\int x sin (\frac{1}{8} x) d x

- 8 x cos (\frac{1}{8} x) + 64 sin (\frac{1}{8} x) + C

Solution steps

\int x sin (\frac{1}{8} x) d x

Apply Integration By Parts

: - 8 x cos (\frac{1}{8} x) - \int - 8 cos (\frac{1}{8} x) d x

= - 8 x cos (\frac{1}{8} x) - \int - 8 cos (\frac{1}{8} x) d x

\int - 8 cos (\frac{1}{8} x) d x = - 64 sin (\frac{1}{8} x)

= - 8 x cos (\frac{1}{8} x) - (- 64 sin (\frac{1}{8} x))

Simplify

= - 8 x cos (\frac{1}{8} x) + 64 sin (\frac{1}{8} x)

Add a constant to the solution

= - 8 x cos (\frac{1}{8} x) + 64 sin (\frac{1}{8} x) + C

\int \frac{( x ^{3} - 6 x - 20 )}{x + 5} d x

y = (x^{4}) + (\frac{3}{( x ^{2} )}), at x = - 1

y^{^{'}} + 2 y = t

e^{- a x^{2}}, x = 0

(x + 1) \cdot \frac{d y}{d x} + y = ln (x)

What is the integral of xsin(1/8 x) ?
The integral of xsin(1/8 x) is -8xcos(1/8 x)+64sin(1/8 x)+C