What is the integral of 4xsin(3x) ?

The integral of 4xsin(3x) is 4(-1/3 xcos(3x)+1/9 sin(3x))+C

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integral of 4xsin(3x)

\int 4 x sin (3 x) d x

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

Solution steps

\int 4 x sin (3 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int x sin (3 x) d x

Apply Integration By Parts

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

= 4 (- \frac{1}{3} x cos (3 x) - \int - \frac{1}{3} cos (3 x) d x)

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

= 4 (- \frac{1}{3} x cos (3 x) - (- \frac{1}{9} sin (3 x)))

Simplify

= 4 (- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x))

Add a constant to the solution

= 4 (- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x)) + C

\int e^{- y} cos (y) d y

y = (x^{2} - 3 x + 3), (2, 1)

\int 45 + 4 x - x^{2} d x

y = (ln (x))^{x}

\int \frac{6 x ^{2} - 3 x}{x ^{2}} d x

What is the integral of 4xsin(3x) ?
The integral of 4xsin(3x) is 4(-1/3 xcos(3x)+1/9 sin(3x))+C