What is the integral of xsin(3x+2) ?

The integral of xsin(3x+2) is -1/3 xcos(3x+2)+1/9 sin(3x+2)+C

Popular >

integral of xsin(3x+2)

\int x sin (3 x + 2) d x

- \frac{1}{3} x cos (3 x + 2) + \frac{1}{9} sin (3 x + 2) + C

Solution steps

\int x sin (3 x + 2) d x

Apply Integration By Parts

: - \frac{1}{3} x cos (3 x + 2) - \int - \frac{1}{3} cos (3 x + 2) d x

= - \frac{1}{3} x cos (3 x + 2) - \int - \frac{1}{3} cos (3 x + 2) d x

\int - \frac{1}{3} cos (3 x + 2) d x = - \frac{1}{9} sin (3 x + 2)

= - \frac{1}{3} x cos (3 x + 2) - (- \frac{1}{9} sin (3 x + 2))

Simplify

= - \frac{1}{3} x cos (3 x + 2) + \frac{1}{9} sin (3 x + 2)

Add a constant to the solution

= - \frac{1}{3} x cos (3 x + 2) + \frac{1}{9} sin (3 x + 2) + C

\frac{d}{d x} (e^{(x - 1)^{2}})

\int \frac{( e ^{2 x} )}{25 + e ^{4 x}} d x

\int e^{x} 7 + e^{x} d x

\int - \frac{1}{262144} cos (8 x) d x

x \to - 3 lim (x^{2} - 8)

What is the integral of xsin(3x+2) ?
The integral of xsin(3x+2) is -1/3 xcos(3x+2)+1/9 sin(3x+2)+C