What is the integral of xsin(5bx) ?

The integral of xsin(5bx) is -1/(5b)xcos(5bx)+1/(25b^2)sin(5bx)+C

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integral of xsin(5bx)

\int x sin (5 b x) d x

- \frac{1}{5 b} x cos (5 b x) + \frac{1}{25 b ^{2}} sin (5 b x) + C

Solution steps

\int x sin (5 b x) d x

Apply Integration By Parts

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

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

\int - \frac{1}{5 b} cos (5 b x) d x = - \frac{1}{25 b ^{2}} sin (5 b x)

= - \frac{1}{5 b} x cos (5 b x) - (- \frac{1}{25 b ^{2}} sin (5 b x))

Simplify

= - \frac{1}{5 b} x cos (5 b x) + \frac{1}{25 b ^{2}} sin (5 b x)

Add a constant to the solution

= - \frac{1}{5 b} x cos (5 b x) + \frac{1}{25 b ^{2}} sin (5 b x) + C

n = 1 \sum \infty \frac{x ^{n}}{5 ^{n}}

y^{^{'}} - \frac{2}{x} y = \frac{y ^{5}}{x ^{2}}, y (1) = 1

\frac{d}{d x} (2 x^{2} + x - 6)

\frac{d}{d x} (cot (6 - x))

\frac{d}{d x} (\frac{sin ( x ) sec ( x )}{1 + x tan ( x )})

What is the integral of xsin(5bx) ?
The integral of xsin(5bx) is -1/(5b)xcos(5bx)+1/(25b^2)sin(5bx)+C