What is the integral of xsin(3x+1) ?

The integral of xsin(3x+1) is -1/3 xcos(3x+1)+1/9 sin(3x+1)+C

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integral of xsin(3x+1)

\int x sin (3 x + 1) d x

- \frac{1}{3} x cos (3 x + 1) + \frac{1}{9} sin (3 x + 1) + C

Solution steps

\int x sin (3 x + 1) d x

Apply Integration By Parts

: - \frac{1}{3} x cos (3 x + 1) - \int - \frac{1}{3} cos (3 x + 1) d x

= - \frac{1}{3} x cos (3 x + 1) - \int - \frac{1}{3} cos (3 x + 1) d x

\int - \frac{1}{3} cos (3 x + 1) d x = - \frac{1}{9} sin (3 x + 1)

= - \frac{1}{3} x cos (3 x + 1) - (- \frac{1}{9} sin (3 x + 1))

Simplify

= - \frac{1}{3} x cos (3 x + 1) + \frac{1}{9} sin (3 x + 1)

Add a constant to the solution

= - \frac{1}{3} x cos (3 x + 1) + \frac{1}{9} sin (3 x + 1) + C

\frac{e ^{- π s}}{s ^{3} + s}

y^{^{'}} = 0.5 x - 450

x \to - 1 lim (\frac{2 - 5 x}{2 + 2 x})

\frac{d}{d x} (3 x^{5} ln (x))

f (x) = \frac{4 x ^{2}}{x + 2}

What is the integral of xsin(3x+1) ?
The integral of xsin(3x+1) is -1/3 xcos(3x+1)+1/9 sin(3x+1)+C