What is the integral of xsin(5x) ?

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

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integral of xsin(5x)

\int x sin (5 x) d x

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

Solution steps

\int x sin (5 x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (arcsin (sin (7 x)))

y = arcsec (\frac{1}{7 t ^{3}})

y = ∣ x - 3 ∣, y = \frac{x}{2}

f (x) = tan (sec (x))

y^{^{''}} + 14 y^{^{'}} + 49 y = 0

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