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

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

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integral of (x+1)sin(3x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{s + 5}{s ^{2} + 4 s + 13}

\frac{d}{d x} (\frac{( x + 3 ) ( x + 1 )}{x ^{2} - 49})

\int_{0}^{1} x cos (π x) d x

\int_{1}^{\infty} x^{- \frac{3}{2}} d x

y^{^{''}} - \frac{2}{x} y^{^{'}} + \frac{2}{x ^{2}} y = 0

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