What is the integral of xsin(1/5 x) ?

The integral of xsin(1/5 x) is -5xcos(1/5 x)+25sin(1/5 x)+C

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integral of xsin(1/5 x)

\int x sin (\frac{1}{5} x) d x

- 5 x cos (\frac{1}{5} x) + 25 sin (\frac{1}{5} x) + C

Solution steps

\int x sin (\frac{1}{5} x) d x

Apply Integration By Parts

: - 5 x cos (\frac{1}{5} x) - \int - 5 cos (\frac{1}{5} x) d x

= - 5 x cos (\frac{1}{5} x) - \int - 5 cos (\frac{1}{5} x) d x

\int - 5 cos (\frac{1}{5} x) d x = - 25 sin (\frac{1}{5} x)

= - 5 x cos (\frac{1}{5} x) - (- 25 sin (\frac{1}{5} x))

Simplify

= - 5 x cos (\frac{1}{5} x) + 25 sin (\frac{1}{5} x)

Add a constant to the solution

= - 5 x cos (\frac{1}{5} x) + 25 sin (\frac{1}{5} x) + C

2 x - 4

\int_{2}^{5} t^{2} ln (3 t) d t

\int t^{2} e^{- 18 t} d t

g (x) = \frac{e ^{x}}{9 e ^{x} + x ^{2}}

\int \frac{x ^{2} - x + 12}{x ^{3} + 3 x} d x

What is the integral of xsin(1/5 x) ?
The integral of xsin(1/5 x) is -5xcos(1/5 x)+25sin(1/5 x)+C