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

The integral of 3xsin(4x) is 3(-1/4 xcos(4x)+1/16 sin(4x))+C

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integral of 3xsin(4x)

\int 3 x sin (4 x) d x

3 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x)) + C

Solution steps

\int 3 x sin (4 x) d x

Take the constant out:

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

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

Apply Integration By Parts

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

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

\int - \frac{1}{4} cos (4 x) d x = - \frac{1}{16} sin (4 x)

= 3 (- \frac{1}{4} x cos (4 x) - (- \frac{1}{16} sin (4 x)))

Simplify

= 3 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x))

Add a constant to the solution

= 3 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x)) + C

\int \frac{1}{( 2 x )} d x

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What is the integral of 3xsin(4x) ?
The integral of 3xsin(4x) is 3(-1/4 xcos(4x)+1/16 sin(4x))+C