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

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

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integral of xcos(3x+1)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int sin^{7} (3 x) d x

\frac{d}{d x} (5 ln (6 - x^{2}))

\frac{d}{d x} (4 x d x)

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 9})

\frac{\partial}{\partial x} ((y - 2) tan (y))

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